Related papers: A generalization of Carter-Payne homomorphisms

This paper introduces calibrated representations for affine Hecke algebras and classifies and constructs all finite dimensional irreducible calibrated representations. The primary technique is to provide indexing sets for controlling the…

Let H be a graded Hecke algebra with complex deformation parameters and Weyl group W. We show that the Hochschild, cyclic and periodic cyclic homologies of H are all independent of the parameters, and compute them explicitly. We use this to…

We generalize a construction of the Neron model for a family of intermediate Jacobians due to Green, Griffiths and Kerr by using the theory of mixed Hodge modules. It is a topological group defined over any partial compactification of the…

Polynomials with values in an irreducible module of the symmetric group can be given the structure of a module for the rational Cherednik algebra, called a standard module. This algebra has one free parameter and is generated by…

We introduce an extended setting to study Hecke pairs $(G,H)$ which admit a regular representation on $L^2(H\backslash G)$, and consequently a $C^*$-algebra. As the result, many pairs of locally compact groups which had been studied in…

We introduce a class of equivalences, which we call generalized semi-infinite Hecke equivalences, between certain categories of representations of graded associative algebras which appear in the setting of semi-infinite cohomology for…

In [11] the authors investigated a family of quotient Hilbert modules in the Cowen-Douglas class over the unit disk constructed from classical Hilbert modules such as the Hardy and Bergman modules. In this paper we extend the results to the…

In math.RT/0304173 the derived category of the principal block in modules over the Lusztig quantum algebra at a root of unity is related to the derived category of equivariant coherent sheaves on the Springer resolution. In the present…

It can be shown that it is possible to find a representation of Hecke algebras within Clifford algebras of multivectors. These Clifford algebras possess a unique gradation and a possibly non-symmetric bilinear form. Hecke algebra…

We introduce Hecke algebras associated to discrete quantum groups with commensurated quantum subgroups. We study their modular properties and the associated Hecke operators. In order to investigate their analytic properties we adapt the…

We settle a long-standing problem in the theory of Hecke algebras of complex reflection groups by constructing many (graded) integral cellular bases of these algebras. As applications, we explicitly construct the simple modules of Ariki's…

In this paper, we define a quotient of the cyclotomic Hecke algebra of type $G(r,1,n)$ as a generalisation of the Temperley-Lieb algebras of type $A$ and $B$. We establish a graded cellular structure for the generalised Temperley-Lieb…

We construct a new family of irreducible modules over any basic classical affine Kac-Moody Lie superalgebra which are induced from modules over the Heisenberg subalgebra. We also obtain irreducible deformations of these modules for the…

We give a Morita equivalence theorem for so-called cyclotomic quotients of affine Hecke algebras of type B and D, in the spirit of a classical result of Dipper-Mathas in type A for Ariki-Koike algebras. As a consequence, the representation…

Let $G$ be a finite group, $H \le G$ a subgroup, $R$ a commutative ring, $A$ an $R$-algebra, and $\alpha$ an action of $G$ on $A$ by $R$-algebra automorphisms. We study the associated \emph{skew Hecke algebra}…

We build on the methods introduced by Friedmann, Hanlon, Stanley, and Wachs, and further developed by Brauner and Friedmann, to construct additional classes of presentations of Specht modules. We obtain these presentations by defining a…

This paper consists of two prongs. Firstly, we prove that any Specht module labelled by a 2-separated partition is semisimple and we completely determine its decomposition as a direct sum of graded simple modules. Secondly, we apply these…

Let H_q(S_n) be the Iwahori-Hecke algebra of the symmetric group. This algebra is semisimple over the rational function field Q(q), where q is an indeterminate, and its irreducible representations over this field are q-analogues S_q(lambda)…

In this note we are interested in labelling the irreducible representations of non-semisimple specialisations of Hecke algebras of complex reflection groups. We will use category O for the rational Cherednik algebra and the KZ functor…

We apply the crystal basis theory for Fock spaces over quantum affine algebras to the modular representations of the cyclotomic Hecke algebras of type $G(p,p,n)$. This yields a classification of simple modules over these cyclotomic Hecke…