Drinfeld twists and symmetric Bethe vectors of supersymmetric fermion models

We construct the Drinfeld twists ( factorizing F-matrices) of the gl(m-n)-invariant fermion model. Completely symmetric representation of the pseudo-particle creation operators of the model are obtained in the basis provided by the F-matrix ( the F-basis). We resolve the hierarchy of the nested Bethe vectors in the F-basis for the gl(m-n) supersymmetric model.

Drinfeld twists and algebraic bethe ansatz of the supersymmetric model associated with U-q(gl(m vertical bar n))

We construct the Drinfeld twists (or factorizing F-matrices) of the supersymmetric model associated with quantum superalgebra U-q(gl(m vertical bar n)), and obtain the completely symmetric representations of the creation operators of the model in the F-basis provided by the F-matrix. As an application of our general results, we present the explicit expressions of the Bethe vectors in the F-basis for the U-q(gl(2 vertical bar 1))-model (the quantum t-J model).

Drinfield twists and alegebraic Bethe ansatz of the supersymmetric t-J model

We construct the Drinfeld twists (factorizing F-matrices) for the supersymmetric t-J model. Working in the basis provided by the F-matrix (i.e. the so-called F-basis), we obtain completely symmetric representations of the monodromy matrix and the pseudo-particle creation operators of the model. These enable us to resolve the hierarchy of the nested Bethe vectors for the gl(2\1) invariant t-J model.

Determinant representations of correlation functions for the supersymmetric t-J model

Working in the F-basis provided by the factorizing F-matrix, the scalar products of Bethe states for the supersymmetric t-J model are represented by determinants. By means of these results, we obtain determinant representations of correlation functions for the model.

On the construction of correlation functions for the integrable supersymmetric fermion models

We review the recent progress on the construction of the determinant representations of the correlation functions for the integrable supersymmetric fermion models. The factorizing F-matrices (or the so-called F-basis) play an important role in the construction. In the F-basis, the creation (and the annihilation) operators and the Bethe states of the integrable models are given in completely symmetric forms. This leads to the determinant representations of the scalar products of the Bethe states for the models. Based on the scalar products, the determinant representations of the correlation functions may be obtained. As an example, in this review, we give the determinant representations of the two-point correlation function for the U-q(gl(2 vertical bar 1)) (i.e. q-deformed) supersymmetric t-J model. The determinant representations are useful for analyzing physical properties of the integrable models in the thermodynamical limit.

On super-RS algebra and Drinfeld realization of quantum affine superalgebras

We describe the realization of the super-Reshetikhin-Semenov-Tian-Shansky (RS) algebra in quantum affine superalgebras, thus generalizing the approach of Frenkel and Reshetikhin to the supersymmetric (and twisted) case. The algebraic homomorphism between the super-RS algebra and the Drinfeld current realization of quantum affine superalgebras is established by using the Gauss decomposition technique of Ding and Frenkel. As an application, we obtain Drinfeld realization of quantum affine superalgebra U-q [osp(1/2)((1))] and its degeneration - central extended super-Yangian double DY(h over bar) [osp(1/2)((1))].

Comments on the Drinfeld realization of the quantum affine superalgebra U-q[gl(m backslash n)(1)] and its Hopf algebra structure

By generalizing the Reshetikhin and Semenov-Tian-Shansky construction to supersymmetric cases, we obtain the Drinfeld current realization for the quantum affine superalgebra U-q[gl(m\n)((1))]. We find a simple coproduct for the quantum current generators and establish the Hopf algebra structure of this super current algebra.

Coefficients of Drinfeld modular forms and Hecke operators

"Vegeu el resum a l'inici del document del fitxer adjunt."

Twists and turns: a tale of two shikimate-pathway enzymes

We are studying two enzymes from the shikimate pathway, dehydroquinate synthase (DHQS) and 5-enolpyruvylshikimate-3-phosphate synthase (EPSPS). Both enzymes have been the subject of numerous studies to elucidate their reaction mechanisms. Crystal structures of DHQS and EPSPS in the presence and absence of substrates, cofactors and/or inhibitors are now available. These structures reveal movements of domains, rearrangements of loops and changes in side-chain positions necessary for the formation of a catalytically competent active site. The potential for using complementary small-angle X-ray scattering (SAXS) studies to confirm the presence of these structural differences in solution has also been explored. Comparative analysis of crystal structures, in the presence and absence of ligands, has revealed structural features critical for substrate-binding and catalysis. We have also analysed these structures by generating GRID energy maps to detect favourable binding sites. The combination of X-ray crystallography, SAXS and computational techniques provides an enhanced analysis of structural features important for the function of these complex enzymes.

COMMUTATIVE ALGEBRAS IN DRINFELD CATEGORIES OF ABELIAN LIE ALGEBRAS

We describe (braided-) commutative algebras with non-degenerate multiplicative form in certain braided monoidal categories, corresponding to abelian metric Lie algebras (so-called Drinfeld categories). We also describe local modules over these algebras and classify commutative algebras with a finite number of simple local modules.

The old problems of glass and the glass transition, and the many new twists.

In this paper I review the ways in which the glassy state is obtained both in nature and in materials science and highlight a "new twist"--the recent recognition of polymorphism within the glassy state. The formation of glass by continuous cooling (viscous slowdown) is then examined, the strong/fragile liquids classification is reviewed, and a new twist-the possibility that the slowdown is a result of an avoided critical point-is noted. The three canonical characteristics of relaxing liquids are correlated through the fragility. As a further new twist, the conversion of strong liquids to fragile liquids by pressure-induced coordination number increases is demonstrated. It is then shown that, for comparable systems, it is possible to have the same conversion accomplished via a first-order transition within the liquid state during quenching. This occurs in the systems in which "polyamorphism" (polymorphism in the glassy state) is observed, and the whole phenomenology is accounted for by Poole's bond-modified van der Waals model. The sudden loss of some liquid degrees of freedom through such weak first-order transitions is then related to the polyamorphic transition between native and denatured hydrated proteins, since the latter are also glass-forming systems--water-plasticized, hydrogen bond-cross-linked chain polymers (and single molecule glass formers). The circle is closed with a final new twist by noting that a short time scale phenomenon much studied by protein physicists-namely, the onset of a sharp change in d/dT ( is the Debye-Waller factor)--is general for glass-forming liquids, including computer-simulated strong and fragile ionic liquids, and is closely correlated with the experimental glass transition temperature. The latter thus originates in strong anharmonicity in certain components of the vibrational density of states, which permits the system to access the multiple minima of its configuration space. The connection between the anharmonicity in these modes, vibrational localization, the Kauzmann temperature, and the fragility of the liquid is proposed as the key problem in glass science.

The crisis in Iraq and the twists and turns of Turkish Middle East policy. OSW Commentary No. 142, 29.07.2014

The spectacular offensive by Islamic radicals in Iraq this June has led the country to the verge of collapse, and is another scene of the deep crisis in the Middle East, in which Turkey is entangled. The immediate consequence of this is a severe crisis of prestige after the kidnapping by terrorists of Turkish diplomats and Ankara’s inability to resolve the situation; in the long term consequences include escalation of the Kurdish problem, and a further increase in threats to the security of Turkey itself as well as the fundamental principles of its foreign policy. Both Ankara’s options and its political will to actively respond to the crisis are extremely limited. Yet again in recent years, the current crisis, the broader situation in the Middle East, and finally the position of Turkey in the region elude unambiguous assessments and forecasts – these are prevented by the scale and growth of the reappraisals and tensions in the region. The only undoubted fact is that Turkey is strategically and irreversibly entangled in the Middle East’s problems, which are an important factor affecting the transformation of the state which the ruling AKP is implementing; and in the near future, this state of affairs will only deepen.

Twists, knots, and rings in proteins: Structural definition of the cyclotide framework

In recent years an increasing number of miniproteins containing an amide-cyclized backbone have been discovered. The cyclotide family is the largest group of such proteins and is characterized by a circular protein backbone and six conserved cysteine residues linked by disulfide bonds in a tight core of the molecule. These form a cystine knot in which an embedded ring formed by two of the disulfide bonds and the connecting backbone segment is threaded by a third disulfide bond. In the current study we have undertaken high resolution structural analysis of two prototypic cyclotides, kalata B1 and cycloviolacin O1, to define the role of the conserved residues in the sequence. We provide the first comprehensive analysis of the topological features in this unique family of proteins, namely rings (a circular backbone), twists (a cis-peptide bond in the Mobius cyclotides) and knots (a knotted arrangement of the disulfide bonds).