We study the local factor at p of the semi-simple zeta function of a Shimura variety of Drinfeld type for a level structure given at p by the pro-unipotent radical of an Iwahori subgroup. Our method is an adaptation to this case of the Langlands-Kottwitz counting method. We explicitly determine the corresponding test functions in suitable Hecke algebras, and show their centrality by determining...

A general method for computing irreducible representations of Weyl groups and Iwahori–Hecke algebras was introduced by the first author in [10]. In that paper the representations of the algebras of typesAn,Bn,Dn andG2 were computed and it is the purpose of this paper to extend these computations to F4. The main goal here is to compute irreducible representations of the Iwahori–Hecke algebra of ...

These are notes for a talk on Kazhdan-Lusztig Cells for Hecke Algebras. In this talk, we construct the Kazhdan-Lusztig basis for the Hecke algebra associated to an arbitrary Coxeter group, in full multiparameter generality. We then use this basis to construct a partition of the Coxeter group into the Kazhdan-Lusztig cells and describe the corresponding cell representations. Finally, we speciali...

We compute the cohomology H∗(H, k) = ExtH(k, k) where H = H(n, q) is the Hecke algebra of the symmetric group Sn at a primitive `th root of unity q, and k is a field of characteristic zero. The answer is particularly interesting when ` = 2, which is the only case where it is not graded commutative. We also carry out the corresponding computation for Hecke algebras of type Bn and Dn when ` is odd.

In this paper, we compute the signatures of the contravariant form on Specht modules for the cyclotomic Hecke algebra and compute the signature character of the contravariant form on the polynomial representation of the rational Cherenik algebra associated toG(r, 1, n).

We construct a family of exact functors from the BGG category O of representations of the Lie algebra sln(C) to the category of finite-dimensional representations of the degenerate (or graded) affine Hecke algebra Hl of GLl. These functors transform Verma modules to standard modules or zero, and simple modules to simple modules or zero. Any simple Hl-module can be thus obtained.

We give a combinatorial description of the composition factors of the induction product of two evaluation modules of the affine Iwahori-Hecke algebra of type GLm. Using quantum affine Schur-Weyl duality, this yields a combinatorial description of the composition factors of the tensor product of two evaluation modules of the quantum affine algebra Uq(ŝln).

Let H be the one-parameter Hecke algebra associated to a finite Weyl group W , defined over a ground ring in which “bad” primes for W are invertible. Using the Kazhdan–Lusztig basis of H, we show that H has a natural cellular structure in the sense of Graham and Lehrer. Previously, this was only known in type An and Bn. Thus, we obtain a general theory of “Specht modules” for Hecke algebras of ...

LetG be a finite group of Lie type (e.g. GLn(Fq)) and U a maximal unipotent subgroup of G. If ψ is a linear character of U , then the unipotent Hecke algebra isHψ = EndCG(Ind G U (ψ)). Unipotent Hecke algebras have a natural basis coming from double cosets of U in G. This paper describes relations for reducing products of basis elements, and gives a detailed description of the implications in t...

Recently Delorme and Opdam have generalized the theory of Rgroups towards affine Hecke algebras with unequal labels. We apply their results in the case where the affine Hecke algebra is of type B, for an induced discrete series representation with real central character. We calculate the R-group of such an induced representation, and show that it decomposes multiplicity free into 2 irreducible ...