Related papers: Construction g\'eometrique de representations de W…

We show that the Weil representation associated with any discriminant form admits a basis in which the action of the representation involves algebraic integers. The action of a general element of $\operatorname{SL}_{2}(\mathbb{Z})$ on many…

We study the automorphism group of the algebraic closure of a substructure A of a pseudo-finite field F, or more generally, of a bounded PAC field F. This paper answers some of the questions of [1], and in particular that any finite group…

For W a finite (2-)reflection group and B its (generalized) braid group, we determine the Zariski closure of the image of B inside the corresponding Iwahori-Hecke algebra. The Lie algebra of this closure is reductive and generated in the…

The present paper deals with the representation theory of the reflection equation algebra, connected with a Hecke type R-matrix. Up to some reasonable additional conditions the R-matrix is arbitrary (not necessary originated from quantum…

All indecomposable finite-dimensional representations of the homogeneous Galilei group which when restricted to the rotation subgroup are decomposed to spin 0, 1/2 and 1 representations are constructed and classified. These representations…

We present a new approach to special lagrangian geometry which works for Bohr - Sommerfeld lagrangian submanifolds of symplectic manifolds with integer symplectic forms. This leads to construction of finite dimensional moduli spaces of SBS…

We compute the image of any choice of complex conjugation on the Galois representations associated to regular algebraic cuspidal automorphic representations and to torsion classes in the cohomology of locally symmetric spaces for $GL_n$…

An axiomatic approach to the representation theory of Coxeter groups and their Hecke algebras was presented in [1]. Combinatorial aspects of this construction are studied in this paper. In particular, the symmetric group case is…

This note extends some results of a previous paper (math.RT/0403250) about finite dimensional representations of the wreath product symplectic reflection algebra H(k,c,N,G) of rank N attached to a finite subgroup G of SL(2,C) (here k is a…

We construct moduli stacks of two-dimensional mod p representations of the absolute Galois group of a p-adic local field, and relate their geometry to the weight part of Serre's conjecture for GL(2).

Given a double vector bundle $D\to M$, we define a bigraded `Weil algebra' $\mathcal{W}(D)$, which `realizes' the algebra of smooth functions on the supermanifold $D[1,1]$. We describe in detail the relations between the Weil algebras of…

Let M be a paracompact smooth manifold of dimension n; A a Weil algebra and M^A the Weil bundle associated. We define and describe the notion of \widetilded-Poisson cohomology and of \widetilded^A -Poisson cohomology on M^A.

We investigate the group structure of center-preserving automorphisms of the finite Heisenberg group over $\mathbb Z_N$ with $U(1)$ extension, which arises in finite-dimensional quantum mechanics on a discrete phase space. Constructing an…

We introduce a wide category of superspaces, called locally finitely generated, which properly includes supermanifolds but enjoys much stronger permanence properties, as are prompted by applications. Namely, it is closed under taking finite…

In this note we present a complete analysis of finite dimensional representations of the Lie superalgebra sl(2|1). This includes, in particular, the decomposition of all tensor products into their indecomposable building blocks. Our…

In this paper we make a clear relationship between the automorphic representations and the quantization through the Geometric Langlands Correspondence. We observe that the discrete series representation are realized in the sum of…

Let $r$ be an odd prime and $\mathbb{F}$ a field containing a primitive $r$th root of unity. Then for all $\ell \geq 1$, there is a faithful representation $f: \operatorname{Sp}_{2\ell}(r) \rightarrow \operatorname{GL}_{r^\ell}(\mathbb{F})$…

Let $G/H$ be a $p$-adic symmetric space. We compute explicitly the higher relative extension groups for all discrete series representations of $G$ in two examples: the symplectic case and the linear case. The results have immediate…

The paper contains a characterization of compact groups $G\subseteq\GL(V)$, where $V$ is a finite dimensional real vector space, which have the following property \SP{}: the family of convex hulls of $G$-orbits is a semigroup with respect…

The transformation behaviour of the vector valued theta function of a positive-definite even lattice under the metaplectic group $\mathrm{Mp}_2(\mathbb{Z})$ is described by the Weil representation. We show that the invariants of this…