Circuits and centralizers in Coxeter groups
by
Patrick Bahls
University of Illinois, Urbana-Champaign

One way to understand the global combinatorial structure of a Coxeter group is to piece together a sufficient amount of local structural information in order to develop a picture of the overall group. To apply this procedure, we must have in hand the appropriate notion of "local", and a means by which the local information can be pieced together.

In this talk we discuss the method of "centralizer chasing", which makes use of the structure of the Coxeter diagram and the form of the centralizer of a fundamental generator. We indicate how this method has been used successfully to prove various structural results about a number of classes of Coxeter groups (including even and two-dimensional groups). We will also demonstrate means by which the method can be applied to yet more general Coxeter groups, yielding information about uniqueness of presentation, subgroup structure, biautomaticity, and automorphism structure of these more general Coxeter groups.

Date received: December 14, 2003