Research Seminar in Mathematics - An introduction to Coxeter groups, the word problem, and twisted involutions

Speaker

Mikael Hansson, Örebro universitet

Abstract

Given a group generated by an alphabet S, the word problem is the problem of deciding whether two words with letters from S represent the same group element. For the important class of Coxeter groups, there is a solution based on the so-called word property, which will be described. I shall motivate and define Coxeter groups, so no knowledge of these groups is assumed. Then, twisted involutions will be introduced. We shall see that in this case, too, there is a word property which solves the word problem.

This talk is based on joint work with Axel Hultman, Linköping University.