Polar orthogonal representations of real reductive algebraic groups

We prove that a polar orthogonal representation of a real reductive algebraic group has the same closed orbits as the isotropy representation of a pseudo-Riemannian symmetric space. We also develop a partial structural theory of polar orthogonal representations of real reductive algebraic groups which slightly generalizes some results of the structural theory of real reductive Lie algebras. (c) 2008 Elsevier Inc. All rights reserved.

TAUT REPRESENTATIONS OF COMPACT SIMPLE LIE GROUPS

The concept of taut submanifold of Euclidean space is due to Carter and West, and can be traced back to the work of Chern and Lashof on immersions with minimal total absolute curvature and the subsequent reformulation of that work by Kuiper in terms of critical point theory. In this paper, we classify the reducible representations of compact simple Lie groups, all of whose orbits are tautly embedded in Euclidean space, with respect to Z(2)-coefficients.

Periodic Higgs-de Rham flows and representations of algebraic fundamental groups

Let k := bar{F}_p for p > 2, W_n(k) := W(k)/p^n and X_n be a projective smooth W_n(k)-scheme which is W_{n+1}(k)-liftable. For all n > 1, we construct explicitly a functor, which we call the inverse Cartier functor, from a subcategory of Higgs bundles over X_n to a subcategory of flat Bundles over X_n. Then we introduce the notion of periodic Higgs-de Rham flows and show that a periodic Higgs-de Rham flow is equivalent to a Fontaine-Faltings module. Together with a p-adic analogue of Riemann-Hilbert correspondence established by Faltings, we obtain a coarse p-adic Simpson correspondence.

Sheaf representations of MV-algebras and lattice-ordered abelian groups via duality

We study representations of MV-algebras -- equivalently, unital lattice-ordered abelian groups -- through the lens of Stone-Priestley duality, using canonical extensions as an essential tool. Specifically, the theory of canonical extensions implies that the (Stone-Priestley) dual spaces of MV-algebras carry the structure of topological partial commutative ordered semigroups. We use this structure to obtain two different decompositions of such spaces, one indexed over the prime MV-spectrum, the other over the maximal MV-spectrum. These decompositions yield sheaf representations of MV-algebras, using a new and purely duality-theoretic result that relates certain sheaf representations of distributive lattices to decompositions of their dual spaces. Importantly, the proofs of the MV-algebraic representation theorems that we obtain in this way are distinguished from the existing work on this topic by the following features: (1) we use only basic algebraic facts about MV-algebras; (2) we show that the two aforementioned sheaf representations are special cases of a common result, with potential for generalizations; and (3) we show that these results are strongly related to the structure of the Stone-Priestley duals of MV-algebras. In addition, using our analysis of these decompositions, we prove that MV-algebras with isomorphic underlying lattices have homeomorphic maximal MV-spectra. This result is an MV-algebraic generalization of a classical theorem by Kaplansky stating that two compact Hausdorff spaces are homeomorphic if, and only if, the lattices of continuous [0, 1]-valued functions on the spaces are isomorphic.

On a Question of Kulshammer for Representations of Finite Groups in Reductive Groups

Peer reviewed

On a Question of Kulshammer for Representations of Finite Groups in Reductive Groups

Peer reviewed

The Real-Quaternionic Indicator of Irreducible Self-Conjugate Representations of Real Reductive Algebraic Groups and A Comment on the Local Langlands Correspondence of GL(2, F )

The real-quaternionic indicator, also called the $\delta$ indicator, indicates if a self-conjugate representation is of real or quaternionic type. It is closely related to the Frobenius-Schur indicator, which we call the $\varepsilon$ indicator. The Frobenius-Schur indicator $\varepsilon(\pi)$ is known to be given by a particular value of the central character. We would like a similar result for the $\delta$ indicator. When $G$ is compact, $\delta(\pi)$ and $\varepsilon(\pi)$ coincide. In general, they are not necessarily the same. In this thesis, we will give a relation between the two indicators when $G$ is a real reductive algebraic group. This relation also leads to a formula for $\delta(\pi)$ in terms of the central character. For the second part, we consider the construction of the local Langlands correspondence of $GL(2,F)$ when $F$ is a non-Archimedean local field with odd residual characteristics. By re-examining the construction, we provide new proofs to some important properties of the correspondence. Namely, the construction is independent of the choice of additive character in the theta correspondence.

Inhabitants' and professionals' social representations of health determinants in a disadvantaged urban area in France: a qualitative analysis = représentations sociales des déterminants de santé dans une zone urbaine défavorisée en France : analyse qualitative auprès d'habitants et de professionnels

Background and objective. - Access to care in French disadvantaged urban areas remains an issue despite the implementation of local healthcare structures. To understand this contradiction, we investigated social representations held by inhabitants of such areas, as well as those of social and healthcare professionals, regarding events or behaviours that can impact low-income individuals' health. Method. - In the context of a health diagnosis, 288 inhabitants living in five disadvantaged districts of Aix-les-Bains, as well as 28 professionals working in these districts, completed an open-ended questionnaire. The two groups of respondents were asked to describe what could have an impact on health status from the inhabitants' point of view. The textual responses were analyzed using the Alceste method. Results. - We observed a number of differences in the way the inhabitants and professionals represented determinants of health in disadvantaged urban areas: the former proposed a representation mixing personal responsibility with physiological, social, familial, and professional aspects, whereas the latter associated health issues with marginalization (financial, drug, or alcohol problems) and personal responsibility. Both inhabitants and professionals mentioned control over events and lifestyle as determinants of health. Discussion. - The results are discussed regarding the consequences of these different representations on the beneficiary - healthcare-provider relationship in terms of communication and trust.

The representations of adolescents about gynecological consultation

Objective: To analyze the social representation of adolescents about gynecological consultation and the influence of those in searching for consultations. Method: Qualitative descriptive study based on the Social Representations Theory, conducted with 50 adolescents in their last year of middle school. The data was collected between April and May of 2010 by Evocations and a Focal Group. The software EVOC and contextual analysis were used in the data treatment. Results: The elements fear and constraint, constant in the central nucleus, can justify the low frequency of adolescents in consultations. The term embarrassment in the peripheral system reinforce current sociocultural norms, while prevention, associated with learning about sex and clarifying doubts, allows to envision an educative function. Obtained testimonies in the focal groups exemplify and reinforce those findings. Conclusion: For an effective health education, professionals, including nurses, need to clarify the youth individually and collectively about their rights to privacy, secrecy, in addition to focus the gynecological consultation as a promotion measure to sexual and reproductive health.

Dynamic social representations of the 2009 H1N1 pandemic: Shifting patterns of sense-making and blame

We investigate dynamics of public perceptions of the 2009 H1N1 influenza pandemic to understand changing patterns of sense-making and blame regarding the outbreak of emerging infectious diseases. We draw on social representation theory combined with a dramaturgical perspective to identify changes in how various collectives are depicted over the course of the pandemic, according to three roles: heroes, villains and victims. Quantitative results based on content analysis of three cross-sectional waves of interviews show a shift from mentions of distant collectives (e.g., far-flung countries) at Wave 1 to local collectives (e.g., risk groups) as the pandemic became of more immediate concern (Wave 2) and declined (Wave 3). Semi-automated content analysis of media coverage shows similar results. Thematic analyses of the discourse associated with collectives revealed that many were consistently perceived as heroes, villains and victims.

On the (un)-ambiguity of adjectival modification in Spanish determiner phrases: informing debates on the mental representations of L2 syntax.

This study contributes to a central debate within contemporary generative second language (L2) theorizing: the extent to which adult learners are (un)able to acquire new functional features that result in a L2 grammar that is mentally structured like the native target (see White, 2003). The adult acquisition of L2 nominal phi-features is explored, with focus on the syntactic and semantic reflexes in the related domain of adjective placement in two experimental groups: English-speaking intermediate (n = 21) and advanced (n = 24) learners of Spanish, as compared to a native-speaker control group (n = 15). Results show that, on some of the tasks, the intermediate L2 learners appear to have acquired the syntactic properties of the Spanish determiner phrase but, on other tasks, to show some delay with the semantic reflexes of prenominal and postnominal adjectives. Crucially, however, our data demonstrate full convergence by all advanced learners and thus provide evidence in contra the predictions of representational deficit accounts (e.g., Hawkins & Chan, 1997; Hawkins & Franceschina, 2004; Hawkins & Hattori, 2006).

Explanations and Representations of Violence by School-age Brazilian Youths

The violence staged by young people has often been subjected to scientific analysis. The way youths speak, in their role as aggressors or as victims, is examined to determine how they experience violence in a number of different spheres. Repeated group interviews are used to analyze how violence is explained and depicted within the family, at school and in the neighbourhood by two groups of young people (14-17 years old) attending the same school on the outskirts of Rio Claro, Sao Paulo, Brazil. One of the groups involved is identified by the school as violent, and the other, as non-violent. Discourse analysis leads to two conclusions. First, the different contexts of violence infuse a mistrust of institutions, the environment and personal relationships into the subjects' experience, forming a fabric that clouds future prospects. Second, the group of youths identified as violent have a more simplistic, pessimistic view of reality: They see the world in black and white, and they lay no stock in the possibility that violence can be avoided. Consequently, they use violence and understand violence as a defensive strategy that gives one identity. On the other hand, the group identified as nonviolent feels it possible to intervene in situations with nonviolent tools like words. For the young subjects, violence is a context that they assume; it cancels their ability to identify rules and institutions, but it does not generate an effective interaction strategy. Violence causes their social microcontext (in which action prevails over meaning or meaning equals action) to assume overblown dimensions. Any intervention strategy must take into account this indissoluble unity between meaning and action.

The discriminants associated to isotropy representations of symmetric spaces

We consider a generalized discriminant associated to a symmetric space which generalizes the discriminant of real symmetric matrices, and note that it can be written as a sum of squares of real polynomials. A method to estimate the minimum number of squares required to represent the discrimininant is developed and applied in examples.

Invariance between subjects of brain wave representations of language

In three experiments, electric brain waves of 19 subjects were recorded under several different experimental conditions for two purposes. One was to test how well we could recognize which sentence, from a set of 24 or 48 sentences, was being processed in the cortex. The other was to study the invariance of brain waves between subjects. As in our earlier work, the analysis consisted of averaging over trials to create prototypes and test samples, to both of which Fourier transforms were applied, followed by filtering and an inverse transformation to the time domain. A least-squares criterion of fit between prototypes and test samples was used for classification. In all three experiments, averaging over subjects improved the recognition rates. The most significant finding was the following. When brain waves were averaged separately for two nonoverlapping groups of subjects, one for prototypes and the other for test samples, we were able to recognize correctly 90% of the brain waves generated by 48 different sentences about European geography.