On the Derived Length of Coxeter Groups

Complete Growth Series of Coxeter Groups with more than Three Generators

Bounding Reflection Length in an Affine Coxeter Group

In any Coxeter group, the conjugates of elements in the standard minimal generating set are called reflections and the minimal number of reflections needed to factor a particular element is called its reflection length. In this article we prove that the reflection length function on an affine Coxeter group has a uniform upper bound. More precisely we prove that the reflection length function on...

Minimal Length Elements in Some Double Cosets of Coxeter Groups

We study the minimal length elements in some double cosets of Coxeter groups and use them to study Lusztig’s G-stable pieces and the generalization of G-stable pieces introduced by Lu and Yakimov. We also use them to study the minimal length elements in a conjugacy class of a finite Coxeter group and prove a conjecture in [GKP].

Involution Statistics in Finite Coxeter Groups

Let W be a finite Coxeter group and X a subset of W . The length polynomial LW,X(t) is defined by LW,X(t) = ∑ x∈X t `(x), where ` is the length function on W . In this article we derive expressions for the length polynomial where X is any conjugacy class of involutions, or the set of all involutions, in any finite Coxeter group W . In particular, these results correct errors in [6] for the invo...

Positive definite functions on Coxeter groups with applications to operator spaces and noncommutative probability

A new class of positive definite functions related to colour-length function on arbitrary Coxeter group is introduced. Extensions of positive definite functions, called the Riesz-Coxeter product, from the Riesz product on the Rademacher (Abelian Coxeter) group to arbitrary Coxeter group is obtained. Applications to harmonic analysis, operator spaces and noncommutative probability is presented. ...