Bill Casselman (University of British Columbia)

Friday 1st December, 12.05-12.55pm, Carslaw 373

Open problems in Coxeter groups and associated structures

I shall list a number of problems that I have come across recently involving Coxeter groups, root systems, Kac-Moody algebras, and associated groups. The basic idea of many of them will be how to encapsulate an infinite structure in a small amount of data. The prototype is the result of Brink and Howlett on the automaticity of Coxeter groups.

As a sample, the following pictures show the weak Bruhat order graph and the Bruhat closure graph for the coset A₂^aff/A₂^fin: