The Kazhdan-Lusztig conjecture for finiteW-algebras

Algebras with Kazhdan-Lusztig theories

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 ...

Twisted Incidence Algebras and Kazhdan-Lusztig-Stanley functions

We introduce a new multiplication in the incidence algebra of a partially ordered set, and study the resulting algebra. As an application of the properties of this algebra we obtain a combinatorial formula for the Kazhdan-Lusztig-Stanley functions of a poset. As special cases this yields new combinatorial formulas for the parabolic and inverse parabolic Kazhdan-Lusztig polyno-mials, for the gen...

Kazhdan-Lusztig-Stanley polynomials and quadratic algebras I M.J.Dyer

In [KL], Kazhdan and Lusztig associate a polynomial to each Bruhat interval in a Coxeter group; some of these “Kazhdan-Lusztig” polynomials now play an important role in several areas of representation theory. A similar family of polynomials has been associated to face latices of convex polytopes (see Stanley [St]). Both families of polynomials remain poorly understood in general, though they a...

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...