Coxeter length

On the Derived Length of Coxeter Groups

We characterize certain properties of the derived series of Coxeter groups by properties of the corresponding Coxeter graphs. In particular, we give necessary and sufficient conditions for a Coxeter group to be quasiperfect.

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].

Maximal Length Elements of Excess Zero in Finite Coxeter Groups

The distribution of descents and length in a Coxeter group

We give a method for computing the q-Eulerian distribution W (t, q) = w∈W t des(w) q l(w) as a rational function in t and q, where (W, S) is an arbitrary Coxeter system, l(w) is the length function in W , and des(w) is the number of simple reflections s ∈ S for which l(ws) < l(w). Using this we compute generating functions encompassing the q-Eulerian distributions of the classical infinite fami...

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...