— In this paper we discuss topics in harmonic analysis and representation theory related to two different real forms G/H and Gc/H of a complex semisimple symmetric space GC/HC. We connect representations of G and G c using the theory of involutive representations of semi-groups and reflection symmetry. We discuss how to generalize the Segal-Bargmann transform to real forms of bounded symmetric ...

Les résultats de cet article concernent leprobì eme de l'existence de représentations d'un groupo¨ıde topologique sur un fibré principal et leur classificationà transformation de jauge près. De telles représentations interviennent naturellement dans divers contextes (théo-ries de jauge classiques ou sur graphe, fibréséquivariants, etc).

— Let p be an odd prime, K a finite extension of Qp and G := Gal(Qp/K) the Galois group. We construct and study filtration structures associated torsion semi-stable representations of G. In particular, we prove that two semi-stable representations share the same p-adic Hodge-Tate type if they are congruent modulo pn with n > c′, where c′ is a constant only depending on K and the differences bet...

Let Qp be an algebraic closure of Qp and C its p-adic completion. Let K be a finite extension of Qp contained in Qp and set GK = Gal(Qp/K). A Qp-representation (resp. a C-representation) of GK is a finite dimensional Qp-vector space (resp. C-vector space) equipped with a linear (resp. semi-linear) continuous action of GK . A banach representation of GK is a topological Qp-vector space, whose to...

Résumé. Nous présentons un processus de construction de descripteurs pour la classification supervisée de séries temporelles. Ce processus est libre de tout paramétrage utilisateur et se décompose en trois étapes : (i) à partir des données originales, nous générons de multiples nouvelles représentations simples ; (ii) sur chacune de ces représentations, nous appliquons un algorithme de cocluste...

— We construct explicitly some analytic families of étale (φ,Γ)-modules, which give rise to analytic families of 2-dimensional crystalline representations. As an application of our constructions, we verify some conjectures of Breuil on the reduction modulo p of those representations, and extend some results (of Deligne, Edixhoven, Fontaine and Serre) on the representations arising from modular ...

— We construct explicitly some analytic families of étale (φ,Γ)-modules, which give rise to analytic families of 2-dimensional crystalline representations. As an application of our constructions, we verify some conjectures of Breuil on the reduction modulo p of those representations, and extend some results (of Deligne, Edixhoven, Fontaine and Serre) on the representations arising from modular ...

We show that the category of representations of the Euclidean group E(2) is equivalent to the category of representations of the preprojective algebra of the quiver of type A∞. Furthermore, we consider the moduli space of E(2)-modules along with a set of generators. We show that these moduli spaces are quiver varieties of the type considered by Nakajima. These identifications allow us to draw o...

— This informal article is an expanded version of two lectures given in Padova during the “Dwork Trimester” in June 2001. Their goal was to explain the proof of the p-adic monodromy theorem for de Rham representations and to give some background on p-adic representations. Résumé. — Cet article informel est une version longue de deux exposés donnés à Padoue en Juin 2001 au “Trimestre Dwork”. Leu...

— The goal of this article is to construct explicitly a p-adic family of representations (which are dihedral representations), to construct their associated (φ,Γ)-modules by writing down explicit matrices for φ and for the action of Γ, and finally to determine which of these are trianguline. Résumé (Une famille p-adique de (φ,Γ)-modules diédraux). — L’objet de cet article est de construire expl...