
School of Mathematics and Statistics
Bill Casselman
University of British Columbia
How to multiply in a Coxeter group.
Friday August 17th, 121pm,
Carslaw 375.
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.
