We use the results on the minimal basis of the centre of an Iwahori-Hecke algebra from our earlier work, as well as some additional results on the minimal basis, to describe the image and kernel of the Brauer homomorphism defined by L. Jones for Iwahori-Hecke algebras of type A.

1.1. Shan has proved that the categories Oc(Wn) for rational Cherednik algebras of type Wn = W (G(`, 1, n)) = Snn(μ`) with n varying, together with decompositions of the parabolic induction and restriction functors of Bezrukavnikov-Etingof, provide a categorification of an integrable s̃le Fock space representation F(m), [18]. The parameters m ∈ Z` and e ∈ N ∪ {∞} arise from the choice of paramet...

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 weight space structure of finite-dimensional modules for the affine Hecke algebra. Using these indexing sets we show that (1) irreducible calibrated representa...

In the representation theory, the classification and the construction of the irreducible representations are essential themes. In the first half of the twentieth century, I. Schur[11] introduced a prominent method to obtain the finite dimensional irreducible representations of the general linear group GL(n,C), or equivalently of its Lie algebra gl(n,C), which we call Schur-Weyl reciprocity at p...

Let R : V ⊗2 → V ⊗2 be a Hecke type solution of the quantum Yang– Baxter equation (a Hecke symmetry). Then, the Hilbert–Poincaré series of the associated R-exterior algebra of the space V is the ratio of two polynomials of degrees m (numerator) and n (denominator). Under the assumption that R is skew-invertible, a rigid quasitensor category SW(V(m|n)) of vector spaces is defined, generated by t...

By assuming the parameter q ∈ C∗ is not a root of unity and introducing the notion of standard Kleshchev multipartitions, we establish a one-to-one correspondence between standard Kleshchev multipartitions and irreducible representations with integral weights of the affine Hecke algebra of type A. Then, on the one hand, we extend the correspondence to all Kleshchev multipartitions for a given A...

For certain algebraic Hecke characters χ of an imaginary quadratic field F we define an Eisenstein ideal in a p-adic Hecke algebra acting on cuspidal automorphic forms of GL2/F . By finding congruences between Eisenstein cohomology classes (in the sense of G. Harder) and cuspidal classes we prove a lower bound for the index of the Eisenstein ideal in the Hecke algebra in terms of the special L-...

A combinatorial construction of a Gelafand model for the symmetric group and its Iwahori-Hecke algebra is presented.

A combinatorial construction of a Gelfand model for the symmetric group and its Iwahori-Hecke algebra is presented.

In this paper we study the branching problems for Hecke algebra H(Dn) of type Dn. We explicitly describe the decompositions of the socle of the restriction of each irreducible H(Dn)-representation to H(Dn−1) into irreducible modules by using the corresponding results for type B Hecke algebras. In particular, we show that any such restrictions are always multiplicity free.