Complements of Coxeter group quotients

On the Poincare Series Associated with Coxeter Group Actions on Complements of Hyperplanes

Let W be a finite Coxeter group, realized as a group generated by reflections in the /-dimensional Euclidean space V. Let s/ be the hyperplane arrangement in C* = F(g)RC consisting of the complexifications of the reflecting hyperplanes of W in V. The hyperplane complement M = Mw = C l — {JHejl/H has been studied by Arnold [1] in the case when W = Sh Brieskorn [3], Deligne [7] and Orlik and Solo...

What Is a Coxeter Group?

Coxeter groups arise in a wide variety of areas, so every mathematician should know some basic facts about them, including their connection to “Dynkin diagrams.” Proofs about these “groups generated by reflections” mainly use group theory, geometry, and combinatorics. This talk will briefly explain: what it means to say that G is a “group generated by reflections” (or, equivalently, that G is a...

On the Center of a Coxeter Group

In this paper, we show that the center of every Coxeter group is finite and isomorphic to (Z2) n for some n ≥ 0. Moreover, for a Coxeter system (W, S), we prove that Z(W ) = Z(W S\S̃) and Z(W S̃ ) = 1, where Z(W ) is the center of the Coxeter group W and S̃ is the subset of S such that the parabolic subgroup W S̃ is the essential parabolic subgroup of (W, S) (i.e. W S̃ is the minimum parabolic subgr...

A Construction of Coxeter Group Representations (II)

An axiomatic approach to the representation theory of Coxeter groups and their Hecke algebras was presented in [1]. Combinatorial aspects of this construction are studied in this paper. In particular, the symmetric group case is investigated in detail. The resulting representations are completely classified and include the irreducible ones.

Longest element of a finite Coxeter group