Algebra Seminar

How to program multiplication in an arbitrary Coxeter group is not at all a trivial matter. The naive approach relies on floating point approximations that may very well fail for groups such as hyperbolic Coxeter groups. A purely combinatorial approach was first devised by Jacques Tits, but although this is useful for short calculations by hand, it is not efficient enough for industrial strength computation. In this talk I will explain how an idea which Fokko du Cloux first proposed for finite groups can be combined with one related to the work of Brink and Howlett on automaticity. In practice this method turns out to be just efficient enough to bootstrap up to an optimal algorithm using one of the structures implicit in the work of Brink and Howlett, the minimal root reflection table.