ON PAIRED ROOT SYSTEMS OF COXETER GROUPS

Root Systems and Coxeter Groups

This is a brief review of root systems and Coxeter groups, intended as background material for a course on double affine Hecke algebras and Macdonald polynomials. They are still incomplete in places. 1. Root systems Much of this material can be found in [Bou]. Let V be a real vector space with a positive definite inner product 〈·, ·〉. If α ∈ V is a non-zero vector, define the reflection sα in t...

Computational Aspects of Root Systems, Coxeter Groups, and Weyl Characters

Root systems for asymmetric geometric representations of Coxeter groups

Root systems for asymmetric geometric representations of Coxeter groups Robert G. Donnelly1 Department of Mathematics and Statistics, Murray State University, Murray, KY 42071 Abstract Results are obtained concerning root systems for asymmetric geometric representations of Coxeter groups. These representations were independently introduced by Vinberg and Eriksson, and generalize the standard ge...

Essays on Coxeter groups Coxeter elements in finite Coxeter groups

A finite Coxeter group possesses a distinguished conjugacy class of Coxeter elements. The literature about these is very large, but it seems to me that there is still room for a better motivated account than what exists. The standard references on thismaterial are [Bourbaki:1968] and [Humphreys:1990], butmy treatment follows [Steinberg:1959] and [Steinberg:1985], from which the clever parts of ...

Rewriting Systems for Coxeter Groups

A finite complete rewriting system for a group is a finite presentation which gives a solution to the word problem and a regular language of normal forms for the group. In this paper it is shown that the fundamental group of an orientable closed surface of genus g has a finite complete rewriting system, using the usual generators a1, .., ag, b1, .., bg along with generators representing their i...