Towards the Kazhdan-Lusztig conjecture

Kazhdan-Lusztig Conjecture and Holonomic Systems

In [7], D. Kazhdan and G. Lusztig gave a conjecture on the multiplicity of simple modules which appear in a Jordan-H61der series of the Verma modules. This multiplicity is described in the terms of Coxeter groups and also by the geometry of Schubert cells in the flag manifold (see [8]). The purpose of this paper is to give the proof of their conjecture. The method employed here is to associate ...

Kazhdan-lusztig Cells

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...

Relative Kazhdan–lusztig Cells

In this paper, we study the Kazhdan–Lusztig cells of a Coxeter group W in a “relative” setting, with respect to a parabolic subgroup WI ⊆ W . This relies on a factorization of the Kazhdan–Lusztig basis {Cw} of the corresponding (multi-parameter) Iwahori–Hecke algebra with respect to WI . We obtain two applications to the “asymptotic case” in type Bn, as introduced by Bonnafé and Iancu: we show ...

Implementation of the Kazhdan–Lusztig algorithm

We denote D the set of parameters (of course the existence of the Cayley transform and cross action tables imply that the set D has already been enumerated, and thus identified with a set [0,M [ of integers.) We let M be the free A-module generated by D, where A = Z[v, v−1], and we write q = v2. We replace the canonical basis (Tδ)δ∈D of M by tδ = v Tδ, where l : D → N is the length function (al...

Algebras with Kazhdan-Lusztig theories