The dominance partial ordering in Coxeter groups
by Xiang Fu
Abstract: In this talk we present new findings concerning a partial ordering, called dominance, defined on the root system of an arbitrary Coxeter group. Dominance was first introduced by Brink and Howlett in their proof that finitely generated Coxeter groups are automatic, and it was later utilized as a tool in general combinatorial and algebraic investigations of Coxeter groups. However, in the literature only the set of roots being minimal with respect to dominance, called elementary roots, were investigated, and in this talk we will describe the behaviour of dominance beyond these elementary roots. Time permitting, we will also outline how dominance in an infinite Coxeter group might be used to describe the possible asymptotic behaviours of (normalized) roots.