Introduction Let G be a connected linear algebraic group over an algebraically closed field K of characteristic p 0. In this paper we determine all finite-dimensional irreducible rational KG-modules V such that G has only a finite number of orbits on the set of vectors in V . We shall call such a

A complete classification and character formulas for finite-dimensional irreducible representations of the rational Cherednik algebra of type A are given. Less complete results for other types are obtained. Links to the geometry of affine flag manifolds and Hilbert schemes are discussed. 1 Main

We construct and study some finite dimensional modules for rational Cherednik algebras for the groups G(r, p, n) by using intertwining operators and a commutative family of operators introduced by Dunkl and Opdam. The coinvariant ring and an analog of the ring constructed by Gordon in the course

Abstract. In this paper, we study representations of the rational Cherednik algebra associated to the complex reflection group G4. In particular, we classify the irreducible finite dimensional representations and compute their characters. 1.

A finite group scheme G over a field k is equivalent to its coordinate algebra, a finite dimensional commutative Hopf algebra k[G] over k. In many contexts, it is natural to consider the rational (or Hochschild) cohomology of G with coefficients in a k[G]-comodule M. This is naturally isomorphic

, so that Lc(triv) is the unique one-dimensional simple Hc-module, then Φ(eLc(triv)) ∼ = OZn, where Zn = τ −1 (0) is the punctual Hilbert scheme. • If c = 1/n + k for k ∈ N then, under a canonical filtration on the finite dimensional module Lc(triv), gr eLc(triv) has a natural bigraded structure

Throughout this paper, except in a few places, let G = the R-rational points on a reductive group defined over R K = a maximal compact subgroup X = the associated symmetric space Let (π, V) be a finite-dimensional algebraic representation of G. Eventually G will be assumed semi-simple and π

of finite-dimensional representations of yangians produce rational solutions of the Yang-Bax...

the irreducible finite-dimensional spherical modules Lν(triv) of H gr ν and of Hratν. We give a formula for the dimension of Lν(triv) and give a geometric interpretation of its

the remainder of this note. By an algebraic number field K, we mean a finite dimensional extension of Q. If K and L are two algebraic number fields satisfying K ⊆ L, then L can be viewed as a K-vector space and we denote its dimension by [L: K]. By the Primitive Element Theorem, there exists a ∈ L such that L