A combinatorial construction of Gelfand models for the symmetric group, for its Iwahori-Hecke algebra and for the hyperoctahedral group is presented.

Let R be a field of any characteristic and A a principal ideal domain. We make a conjecture that asserts that any Hecke operator T acts punctually on any Hecke eigenclass in the stable homology with trivial coefficients R of a principal congruence subgroup Γ in GL(n, A), i.e. as multiplication by the number of single cosets contained in T . In the case where A = Z, this conjecture implies that ...

In the previous part of this paper, we constructed a large family of Hecke algebras on some classical groups G de¢ned over p-adic ¢elds in order to understand their admissible representations. EachHecke algebra is associated to a pair …JS; rS†of an open compact subgroup JS and its irreducible representation rSwhich is constructed fromgiven dataS ˆ …G;P0 0; R†. Here, G is a semisimple element in...

We give a polynomial basis of each irreducible representation of the Hecke algebra, as well as an adjoint basis. Decompositions in these bases are obtained by mere specializations.

We prove that the determinant (generalized pseudocharacter) associated to the Hecke algebra of Katz modular forms of weight one and level prime to p is unramified at p.

Given a Hecke symmetry R, one can define a matrix bialgebra ER and a matrix Hopf algebra HR, which are called function rings on the matrix quantum semi-group and matrix quantum groups associated to R. We show that for an even Hecke symmetry, the rational representations of the corresponding quantum group are absolutely reducible and that the fusion coefficients of simple representations depend ...

The Temperley-Lieb algebra may be thought of as a quotient of the Hecke algebra of type A, acting on tensor space as the commutant of the usual action of quantum sl2 on (C(q) ). We define and study a quotient of the BirmanWenzl-Murakami algebra, which plays an analogous role for the 3-dimensional representation of quantum sl2. In the course of the discussion we prove some general results about ...

In this article we work with the degenerate affine Hecke algebra Hl corresponding to the general linear group GLl over a local non-Archimedean field. This algebra was introduced by V.Drinfeld in [D], see also [L]. The complex associative algebra Hl is generated by the symmetric group algebra CSl and by the pairwise commuting elements x1 , . . . , xl with the cross relations for p = 1 , . . . , ...

The degenerate affine Hecke algebra (dAHA) of any finite Coxeter group was defined by Drinfeld and Lusztig([Dri],[Lus]). It is generated by the group algebra of the Coxeter group and by the commuting generators yi with some relations. In [AS], the authors give a Lie-theoretic construction of representations of the dAHA of type An−1. They construct a functor from the BGG category of slN to the c...