0-Hecke algebras of finite Coxeter groups

in Algebra . Coxeter groups and Hecke algebras

The finite Coxeter groups are the finite groups generated by reflections on real Euclidean spaces. Examples include dihedral groups, the symmetry groups of regular polytopes (e.g. regular polygons and platonic solids) and the Weyl groups of semisimple complex Lie groups and Lie algebras (such as the special linear group and Lie algebra). General Coxeter groups may be defined as certain (special...

Coxeter Construction for Hecke Algebras

`good' Elements of Finite Coxeter Groups and Representations of Iwahori{hecke Algebras

Positivity results for the Hecke algebras of non-crystallographic finite Coxeter groups

This paper is a report on a computer check of some important positivity properties of the Hecke algebra in type H4, including the nonnegativity of the structure constants in the Kazhdan-Lusztig basis. This answers a long-standing question of Lusztig’s. The same algorithm, carried out by hand, also allows us to deal with the case of dihedral Coxeter groups. 1 Statement of the problem 1.1. Let W ...

Hecke Algebras and Representations of Finite Reductive Groups

Let F be a eld and G a nite group. Choosing a suitable Mackey system of subfactors of G one can subdivide the irreducible FG-modules into series labelled by semisimple Harish-Chandra vertices and sources. This reduces the classiication problem for irreducible FG-modules partially to the problem of nding the irreducible representations of certain endomorphism rings of Harish-Chandra induced modu...