Toeplitz operators on finite and infinite dimensional spaces with associated psi *-Fréchet algebras

The present thesis is a contribution to the multi-variable theory of Bergman and Hardy Toeplitz operators on spaces of holomorphic functions over finite and infinite dimensional domains. In particular, we focus on certain spectral invariant Frechet operator algebras F closely related to the local symbol behavior of Toeplitz operators in F. We summarize results due to B. Gramsch et.al. on the construction of Psi_0- and Psi^*-algebras in operator algebras and corresponding scales of generalized Sobolev spaces using commutator methods, generalized Laplacians and strongly continuous group actions. In the case of the Segal-Bargmann space H^2(C^n,m) of Gaussian square integrable entire functions on C^n we determine a class of vector-fields Y(C^n) supported in complex cones K. Further, we require that for any finite subset V of Y(C^n) the Toeplitz projection P is a smooth element in the Psi_0-algebra constructed by commutator methods with respect to V. As a result we obtain Psi_0- and Psi^*-operator algebras F localized in cones K. It is an immediate consequence that F contains all Toeplitz operators T_f with a symbol f of certain regularity in an open neighborhood of K. There is a natural unitary group action on H^2(C^n,m) which is induced by weighted shifts and unitary groups on C^n. We examine the corresponding Psi^*-algebra A of smooth elements in Toeplitz-C^*-algebras. Among other results sufficient conditions on the symbol f for T_f to belong to A are given in terms of estimates on its Berezin-transform. Local aspects of the Szegö projection P_s on the Heisenbeg group and the corresponding Toeplitz operators T_f with symbol f are studied. In this connection we apply a result due to Nagel and Stein which states that for any strictly pseudo-convex domain U the projection P_s is a pseudodifferential operator of exotic type (1/2, 1/2). The second part of this thesis is devoted to the infinite dimensional theory of Bergman and Hardy spaces and the corresponding Toeplitz operators. We give a new proof of a result observed by Boland and Waelbroeck. Namely, that the space of all holomorphic functions H(U) on an open subset U of a DFN-space (dual Frechet nuclear space) is a FN-space (Frechet nuclear space) equipped with the compact open topology. Using the nuclearity of H(U) we obtain Cauchy-Weil-type integral formulas for closed subalgebras A in H_b(U), the space of all bounded holomorphic functions on U, where A separates points. Further, we prove the existence of Hardy spaces of holomorphic functions on U corresponding to the abstract Shilov boundary S_A of A and with respect to a suitable boundary measure on S_A. Finally, for a domain U in a DFN-space or a polish spaces we consider the symmetrizations m_s of measures m on U by suitable representations of a group G in the group of homeomorphisms on U. In particular,in the case where m leads to Bergman spaces of holomorphic functions on U, the group G is compact and the representation is continuous we show that m_s defines a Bergman space of holomorphic functions on U as well. This leads to unitary group representations of G on L^p- and Bergman spaces inducing operator algebras of smooth elements related to the symmetries of U.

On moduli spaces of semistable sheaves on K3 surfaces

Ich untersuche die nicht bereits durch die Arbeit "Singular symplectic moduli spaces" von Kaledin, Lehn und Sorger (Invent. Math. 164 (2006), no. 3) abgedeckten Fälle von Modulräumen halbstabiler Garben auf projektiven K3-Flächen - die Fälle mit Mukai-Vektor (0,c,0) sowie die Modulräume zu nichtgenerischen amplen Divisoren - hinsichtlich der möglichen Konstruktion neuer Beispiele von kompakten irreduziblen symplektischen Mannigfaltigkeiten. Ich stelle einen Zusammenhang zu den bereits untersuchten Modulräumen und Verallgemeinerungen derselben her und erweitere bekannte Ergebnisse auf alle offenen Fälle von Garben vom Rang 0 und viele Fälle von Garben von positivem Rang. Insbesondere kann in diesen Fällen die Existenz neuer Beispiele von kompakten irreduziblen symplektischen Mannigfaltigkeiten, die birational über Komponenten des Modulraums liegen, ausgeschlossen werden.

Quantum Integrability in Non-Linear Sigma Models related to Gauge/String Correspondences

The Thermodynamic Bethe Ansatz analysis is carried out for the extended-CP^N class of integrable 2-dimensional Non-Linear Sigma Models related to the low energy limit of the AdS_4xCP^3 type IIA superstring theory. The principal aim of this program is to obtain further non-perturbative consistency check to the S-matrix proposed to describe the scattering processes between the fundamental excitations of the theory by analyzing the structure of the Renormalization Group flow. As a noteworthy byproduct we eventually obtain a novel class of TBA models which fits in the known classification but with several important differences. The TBA framework allows the evaluation of some exact quantities related to the conformal UV limit of the model: effective central charge, conformal dimension of the perturbing operator and field content of the underlying CFT. The knowledge of this physical quantities has led to the possibility of conjecturing a perturbed CFT realization of the integrable models in terms of coset Kac-Moody CFT. The set of numerical tools and programs developed ad hoc to solve the problem at hand is also discussed in some detail with references to the code.

The geometry of Lagrangian fibres

If the generic fibre f−1(c) of a Lagrangian fibration f : X → B on a complex Poisson– variety X is smooth, compact, and connected, it is isomorphic to the compactification of a complex abelian Lie–group. For affine Lagrangian fibres it is not clear what the structure of the fibre is. Adler and van Moerbeke developed a strategy to prove that the generic fibre of a Lagrangian fibration is isomorphic to the affine part of an abelian variety.rnWe extend their strategy to verify that the generic fibre of a given Lagrangian fibration is the affine part of a (C∗)r–extension of an abelian variety. This strategy turned out to be successful for all examples we studied. Additionally we studied examples of Lagrangian fibrations that have the affine part of a ramified cyclic cover of an abelian variety as generic fibre. We obtained an embedding in a Lagrangian fibration that has the affine part of a C∗–extension of an abelian variety as generic fibre. This embedding is not an embedding in the category of Lagrangian fibrations. The C∗–quotient of the new Lagrangian fibration defines in a natural way a deformation of the cyclic quotient of the original Lagrangian fibration.

Entanglement entropy in 1-d quantum spin chains

In questa tesi abbiamo studiato il comportamento delle entropie di Entanglement e dello spettro di Entanglement nel modello XYZ attraverso delle simulazioni numeriche. Le formule per le entropie di Von Neumann e di Renyi nel caso di una catena bipartita infinita esistevano già, ma mancavano ancora dei test numerici dettagliati. Inoltre, rispetto alla formula per l'Entropia di Entanglement di J. Cardy e P. Calabrese per sistemi non critici, tali relazioni presentano delle correzioni che non hanno ancora una spiegazione analitica: i risultati delle simulazioni numeriche ne hanno confermato la presenza. Abbiamo inoltre testato l'ipotesi che lo Schmidt Gap sia proporzionale a uno dei parametri d'ordine della teoria, e infine abbiamo simulato numericamente l'andamento delle Entropie e dello spettro di Entanglement in funzione della lunghezza della catena di spin. Ciò è stato possibile solo introducendo dei campi magnetici ''ad hoc'' nella catena, con la proprietà che l'andamento delle suddette quantità varia a seconda di come vengono disposti tali campi. Abbiamo quindi discusso i vari risultati ottenuti.

Spectral theory of differential operators on finite metric graphs and on bounded domains

Die vorliegende Arbeit widmet sich der Spektraltheorie von Differentialoperatoren auf metrischen Graphen und von indefiniten Differentialoperatoren auf beschränkten Gebieten. Sie besteht aus zwei Teilen. Im Ersten werden endliche, nicht notwendigerweise kompakte, metrische Graphen und die Hilberträume von quadratintegrierbaren Funktionen auf diesen betrachtet. Alle quasi-m-akkretiven Laplaceoperatoren auf solchen Graphen werden charakterisiert, und Abschätzungen an die negativen Eigenwerte selbstadjungierter Laplaceoperatoren werden hergeleitet. Weiterhin wird die Wohlgestelltheit eines gemischten Diffusions- und Transportproblems auf kompakten Graphen durch die Anwendung von Halbgruppenmethoden untersucht. Eine Verallgemeinerung des indefiniten Operators $-tfrac{d}{dx}sgn(x)tfrac{d}{dx}$ von Intervallen auf metrische Graphen wird eingeführt. Die Spektral- und Streutheorie der selbstadjungierten Realisierungen wird detailliert besprochen. Im zweiten Teil der Arbeit werden Operatoren untersucht, die mit indefiniten Formen der Art $langlegrad v, A(cdot)grad urangle$ mit $u,vin H_0^1(Omega)subset L^2(Omega)$ und $OmegasubsetR^d$ beschränkt, assoziiert sind. Das Eigenwertverhalten entspricht in Dimension $d=1$ einer verallgemeinerten Weylschen Asymptotik und für $dgeq 2$ werden Abschätzungen an die Eigenwerte bewiesen. Die Frage, wann indefinite Formmethoden für Dimensionen $dgeq 2$ anwendbar sind, bleibt offen und wird diskutiert.

Fontaine modules and F-T-crystals, a dévissage

Das Hauptziel der Arbeit ist es, die Beziehung zwischen Fontaine Modulen und F-T-Kristall zu studieren. Im ersten Kapitel wird die Definition von Fontaine Modulen, die auf die inversen Cartier Transform setzt erinnern wir von Ogus und Vologodsky errichtet. Neben der Erinnerung an die urspruengliche Konstruktion des inversen Cartier Transform, eine direktere Konstruktion, die wir auch vorstellen von G.T. Lan, M. Sheng und K. Zuo. Darueber hinaus beweisen wir diernGleichwertigkeit der beiden Konstruktion.rnrnrnIm zweiten Kapitel werden wir uns daran erinnern, den Konstruktion von inversen Cartier Transform in der Log Einstellung von D. Schepler und verallgemeinern die Lan-Sheng-Zuo Konstruktion an dieser Einstellung. Darueber hinaus geben wir eine Definition von Log FontainernModulen. Im dritten Kapitel werden wir erinnern an die Definition von F-T-Kristall und beweisen das wichtigste Ergebnis dieser Arbeit: Sei $Y$ eine glatte $S_{nu}$-Schema, wobei $S_{nu}$ ist eine flache $W_{nu+1}(k)$-Schema, $nugeq1$, und $X/S_0$ seine Reduction modulo $p$ sein. Bei einem F-T-Kristall $(E,Phi,B)$ auf $Y$ der Breite von weniger als $p$ und let $(E_Y ,B_Y ,nabla_Y)$ die entsprechende gefilterte $O_Y$-modulen mit einer integrierbar Zusammenhang ausgestattet. Anschliesend wird die Reduktion dieses Objekt modulo $p$ definiert eine Fontaine Modulen auf $X/S_0$ im dem Sinnernder Ogus und Vologodsky.

Applications of elliptic functions to solve differential equations

In questa tesi si mostrano alcune applicazioni degli integrali ellittici nella meccanica Hamiltoniana, allo scopo di risolvere i sistemi integrabili. Vengono descritte le funzioni ellittiche, in particolare la funzione ellittica di Weierstrass, ed elenchiamo i tipi di integrali ellittici costruendoli dalle funzioni di Weierstrass. Dopo aver considerato le basi della meccanica Hamiltoniana ed il teorema di Arnold Liouville, studiamo un esempio preso dal libro di Moser-Integrable Hamiltonian Systems and Spectral Theory, dove si prendono in considerazione i sistemi integrabili lungo la geodetica di un'ellissoide, e il sistema di Von Neumann. In particolare vediamo che nel caso n=2 abbiamo un integrale ellittico.

Porous silicon technology for integrated microsystems

With the development of micro systems, there is an increasing demand for integrable porous materials. In addition to those conventional applications, such as filtration, wicking, and insulating, many new micro devices, including micro reactors, sensors, actuators, and optical components, can benefit from porous materials. Conventional porous materials, such as ceramics and polymers, however, cannot meet the challenges posed by micro systems, due to their incompatibility with standard micro-fabrication processes. In an effort to produce porous materials that can be used in micro systems, porous silicon (PS) generated by anodization of single crystalline silicon has been investigated. In this work, the PS formation process has been extensively studied and characterized as a function of substrate type, crystal orientation, doping concentration, current density and surfactant concentration and type. Anodization conditions have been optimized for producing very thick porous silicon layers with uniform pore size, and for obtaining ideal pore morphologies. Three different types of porous silicon materials: meso porous silicon, macro porous silicon with straight pores, and macro porous silicon with tortuous pores, have been successfully produced. Regular pore arrays with controllable pore size in the range of 2µm to 6µm have been demonstrated as well. Localized PS formation has been achieved by using oxide/nitride/polysilicon stack as masking materials, which can withstand anodization in hydrofluoric acid up to twenty hours. A special etching cell with electrolytic liquid backside contact along with two process flows has been developed to enable the fabrication of thick macro porous silicon membranes with though wafer pores. For device assembly, Si-Au and In-Au bonding technologies have been developed. Very low bonding temperature (~200 degrees C) and thick/soft bonding layers (~6µm) have been achieved by In-Au bondi ng technology, which is able to compensate the potentially rough surface on the porous silicon sample without introducing significant thermal stress. The application of the porous silicon material in micro systems has been demonstrated in a micro gas chromatograph system by two indispensable components: an integrated vapor source and an inlet filter, wherein porous silicon performs the basic functions of porous media: wicking and filtration. By utilizing a macro porous silicon wick, the calibration vapor source was able to produce a uniform and repeatable vapor generation for n-decane with less than a 0.1% variation in 9 hours, and less than a 0.5% variation in rate over 7 days. With engineered porous silicon membranes the inlet filter was able to show a depth filtration with nearly 100% collection efficiency for particles larger than 0.3µm in diameter, a low pressure-drop of 523Pa at 20sccm flow rate, and a filter capacity of 500µg/cm2.

Large deviations for heavy-tailed random elements in convex cones

We prove large deviation results for sums of heavy-tailed random elements in rather general convex cones being semigroups equipped with a rescaling operation by positive real numbers. In difference to previous results for the cone of convex sets, our technique does not use the embedding of cones in linear spaces. Examples include the cone of convex sets with the Minkowski addition, positive half-line with maximum operation and the family of square integrable functions with arithmetic addition and argument rescaling.

Infinite Transitivity on Affine Varieties

In this note we survey recent results on automorphisms of affine algebraic varieties, infinitely transitive group actions and flexibility. We present related constructions and examples, and discuss geometric applications and open problems.

Flexibility Properties in Complex Analysis and Affine Algebraic Geometry

In the last decades affine algebraic varieties and Stein manifolds with big (infinite-dimensional) automorphism groups have been intensively studied. Several notions expressing that the automorphisms group is big have been proposed. All of them imply that the manifold in question is an Oka–Forstnerič manifold. This important notion has also recently merged from the intensive studies around the homotopy principle in Complex Analysis. This homotopy principle, which goes back to the 1930s, has had an enormous impact on the development of the area of Several Complex Variables and the number of its applications is constantly growing. In this overview chapter we present three classes of properties: (1) density property, (2) flexibility, and (3) Oka–Forstnerič. For each class we give the relevant definitions, its most significant features and explain the known implications between all these properties. Many difficult mathematical problems could be solved by applying the developed theory, we indicate some of the most spectacular ones.

Yang-Baxter deformations of Minkowski spacetime

We study Yang-Baxter deformations of 4D Minkowski spacetime. The Yang-Baxter sigma model description was originally developed for principal chiral models based on a modified classical Yang-Baxter equation. It has been extended to coset curved spaces and models based on the usual classical Yang-Baxter equation. On the other hand, for flat space, there is the obvious problem that the standard bilinear form degenerates if we employ the familiar coset Poincaré group/Lorentz group. Instead we consider a slice of AdS5 by embedding the 4D Poincaré group into the 4D conformal group SO(2, 4) . With this procedure we obtain metrics and B-fields as Yang-Baxter deformations which correspond to well-known configurations such as T-duals of Melvin backgrounds, Hashimoto-Sethi and Spradlin-Takayanagi-Volovich backgrounds, the T-dual of Grant space, pp-waves, and T-duals of dS4 and AdS4. Finally we consider a deformation with a classical r-matrix of Drinfeld-Jimbo type and explicitly derive the associated metric and B-field which we conjecture to correspond to a new integrable system.

Examples of PDEs all whose points are characteristic

Let π : FM ! M be the bundle of linear frames of a manifold M. A basis Lijk , j < k, of diffeomorphism invariant Lagrangians on J1 (FM) was determined in [J. Muñoz Masqué, M. E. Rosado, Invariant variational problems on linear frame bundles, J. Phys. A35 (2002) 2013-2036]. The notion of a characteristic hypersurface for an arbitrary first-order PDE system on an ar- bitrary bred manifold π : P → M, is introduced and for the systems dened by the Euler-Lagrange equations of Lijk every hypersurface is shown to be characteristic. The Euler-Lagrange equations of the natural basis of Lagrangian densities Lijk on the bundle of linear frames of a manifold M which are invariant under diffeomorphisms, are shown to be an underdetermined PDEs systems such that every hypersurface of M is characteristic for such equations. This explains why these systems cannot be written in the Cauchy-Kowaleska form, although they are known to be formally integrable by using the tools of geometric theory of partial differential equations, see [J. Muñoz Masqué, M. E. Rosado, Integrability of the eld equations of invariant variational problems on linear frame bundles, J. Geom. Phys. 49 (2004), 119-155]

Solución para la delegación de identidad en Sistemas de Gestión de Identidad paneuropeos basada en infraestructuras de certificación y lenguajes formales de asertos de seguridad

La estrategia i2010 de la UE tiene como objetivo garantizar el liderazgo europeo en materia de TIC y poner los beneficios de la Sociedad de la Información al servicio de la economía, la sociedad y la calidad de vida personal, teniendo presente que los éxitos de Europa hasta la fecha se han basado en favorecer la competencia leal en los mercados de las telecomunicaciones y crear un mercado sin fronteras para contenidos y medios de comunicación digitales. En esta línea, la Comisión Europea ha establecido que los distintos estados miembros deben contribuir activamente al desarrollo y uso seguro de los servicios telemáticos entre sus ciudadanos. Más concretamente, atribuye a las Administraciones Públicas, tanto a nivel nacional, regional como local, un papel dinamizador de la Sociedad de la Información que les obliga a ofrecer paulatinamente todos los actos administrativos a los ciudadanos a través de Internet. Como primer paso para el uso seguro de los servicios telemáticos que ofrecen las instituciones públicas se hace preciso dotar a los ciudadanos de una identidad digital que les permita identificarse ante un Proveedor de Servicio o ante otros ciudadanos de manera inequívoca. Por esta razón, la mayoría de países europeos – y otros en el resto del mundo – están promoviendo, sistemas fiables de gestión de identidad electrónica (eIDM), de tal manera que los ciudadanos, las empresas y departamentos gubernamentales (incluso en Estados miembros diferentes) pueden identificar y certificar sus operaciones con precisión, rapidez y sencillez. Sin embargo, la gestión de esta identidad por las Administraciones Públicas supone un importante desafío, acentuado cuando se hace necesaria la interoperabilidad entre Administraciones de diferentes países, puesto que personas y entidades tienen credenciales de identificación diferentes en función de su propio marco jurídico nacional. Consciente del problema, en la Unión Europea se han puesto en marcha una serie de proyectos con el objetivo de conseguir la interoperabilidad de los eIDMs entre las instituciones públicas de diferentes Estados miembros. A pesar de ello, las soluciones adoptadas hasta la fecha son insuficientes porque no prevén todos los posibles casos de interacción del usuario con las instituciones. En concreto, no tienen en cuenta un aspecto muy importante que se ofrece en los distintos sistemas jurídicos nacionales, a saber, la delegación de la identidad, mediante la cual un ciudadano puede autorizar a otro para que actúe en su nombre para acceder a determinados servicios prestados por las instituciones públicas. En esta tesis se realizan un conjunto de aportaciones que dan solución a distintos aspectos de los problemas planteados y que, de forma conjunta, permiten la interoperabilidad y la delegación de identidad en determinados Sistemas de Gestión de Identidad aplicados al entorno de las Administraciones Públicas. En el caso de la delegación, se ha definido un sistema de delegación dinámica de identidad entre dos entidades genéricas que permite solucionar el problema del acceso delegado a los servicios telemáticos ofrecidos por las Administraciones Públicas. La solución propuesta se basa en la generación de un token de delegación, constituido a partir de un Certificado Proxy, que permite a la entidad que delega establecer la delegación de identidad en otra entidad en base a un subconjunto de sus atributos como delegador, estableciendo además, en el propio token de delegación, restricciones en el conjunto de servicios accesibles a la entidad delegada y el tiempo de validez de la delegación. Adicionalmente, se presentan los mecanismos necesarios tanto para poder revocar un token de delegación como para comprobar sin un token de delegación ha sido o no revocado. Para ello se propone una solución para la identificación unívoca de tokens de delegación y la creación de una nueva entidad denominada Autoridad de Revocación de Tokens de Delegación. Entre las características del sistema de delegación propuesto destaca el que es lo suficientemente seguro como para ser utilizado en el entorno de la Administración Pública, que no requiere el uso de mecanismos off‐line para la generación de la delegación y que se puede realizar la delegación de forma instantánea y sin la necesidad de trámites complejos o la participación de un elevado número de entidades. Adicionalmente, el token de delegación propuesto es perfectamente integrable en las infraestructura de clave pública actual lo que hace que, dado que gran parte de las Administraciones Públicas europeas basan sus sistemas de identidad digital en el uso de la PKI y certificados de identidad X.509, la solución pueda ser puesta en marcha en un entorno real sin necesidad de grandes cambios o modificaciones de comportamiento. En lo referente a la interoperabilidad, se realiza un análisis exhaustivo y la correspondiente evaluación de las principales propuestas de Sistemas de Gestión de Identidad orientados a conseguir la interoperabilidad realizadas hasta la fecha en el marco de la Unión Europea y se propone, a alto nivel, una arquitectura de interoperabilidad para la gestión de identidad en las Administraciones Públicas. Dicha arquitectura es lo suficientemente genérica como para poder ser aplicada tanto en el entorno pan‐Europeo como en los entornos nacionales, autonómicos y locales, de tal forma que la interoperabilidad en la gestión de la identidad esté garantizada en todos los niveles de la Administración Pública. Por último, mediante la integración de la solución de delegación dinámica de identidad y la arquitectura de interoperabilidad propuestas se presenta una solución al problema de la delegación en un escenario pan‐Europeo de gestión de identidad, dando lugar a una arquitectura global de interoperabilidad pan‐Europea con soporte a la delegación de identidad. SUMMARY The i2010 European Union Plan aims to ensure European leadership in ICT and to promote the positive contribution that information and communication technologies can make to the economic, social and personal quality of life, bearing in mind that, to date, success in Europe has been based on promoting fair competition in telecommunications markets and on creating a borderless market for contents and digital media. In this line, the European Commission has established that the different member states should contribute actively to the development and secure use of telematic services among their citizens. More specifically, it is attributed to national, regional and local Public Administrations to have a supportive role of the Information Society, requiring them to gradually provide the citizens with Internet‐based access to all administrative procedures acts. As a first step for the secure use of telematic services offered by public institutions, it is necessary to provide the citizens with a digital identity to enable them to identify themselves unequivocally to a Service Provider or to other citizens. For this reason, most European countries ‐ and others in the rest of the world ‐ are promoting reliable systems for managing electronic identity (eIDM), so that citizens, businesses and government departments (even in different Member States) can identify and certify their operations with precision, speed and simplicity. However, the identity management by Public Administrations is a major challenge that becomes more difficult when interoperability between administrations of different countries is needed, due to the fact that individuals and entities have different identification credentials according to their own national legal framework. Aware of the problem, the European Union has launched a series of projects with the aim of achieving interoperability of eIDMs between public institutions of different Member States. However, the solutions adopted to date are insufficient because they do not foresee all possible cases of user interaction with the institutions. In particular, solutions do not take into account a very important aspect that is offered in different national legal systems, namely, the delegation of identity, by which a citizen can authorize another to act on his/her behalf to access certain services provided by public institutions. In this thesis a collection of contributions that provide solution to different aspects of the aforementioned problems are carried out. The solutions, in global, enable interoperability and identity delegation in some of the Identity Management Systems applied to Public Administration environment. In the case of delegation, a dynamic identity delegation system between generic entities is defined. This system makes it possible to solve the problem of delegated access to telematic services offered by Public Administrations. The proposed solution is based on the generation of a piece of information called delegation token. This delegation token, derived from a Proxy Certificate, allows the establishment of identity delegation by an entity that delegates (delegator) in other entity (delegatee) making use of a subset of delegator attributes. It also establishes restrictions on services that can be used by the delegated entity and the expiry date of delegation. In addition to this, the mechanisms necessary to revoke and check the revocation status of a delegation token are presented. To do this, a solution to univocally identify delegation tokens and the creation of a completely new entity, called Token Delegation Revocation Authority, are proposed. The most remarkable characteristics of the proposed delegation system are its security, enough for it to be used in the Public Administration environment, the fact that it does not require off‐line processes in order to generate the delegation, and the possibility of performing the delegation instantaneously and without neither complex processes nor the intervention of a large number of entities. The proposed delegation token can be completely incorporated into current Public Key Infrastructure (PKI). Thus, since most of the European Public Administrations base their digital identity systems on PKI and X.509 identity certificates, the solution can be adopted in a real environment without great changes or performance modifications. Regarding interoperability, an exhaustive analysis and evaluation of most significant proposals on Identity Management Systems that aim to achieve interoperability carried out in the European Union framework until now are performed. A high level identity management interoperability architecture for Public Administrations is also proposed. This architecture is sufficiently generic to be applied to both pan‐European environment and national, regional or local environments, thus interoperability in identity management at all Public Administration levels is guaranteed. Finally, through the integration of the proposed dynamic identity delegation solution and the high level interoperability architecture, a solution to the problem of identity delegation in a pan‐European identity management environment is suggested, leading to a pan‐European global interoperability architecture with identity delegation support.