In this talk we present a few 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 make attempts to describe the behaviour of dominance beyond these elementary roots. Time permitting, we will also outline how dominance in an arbitrary Coxeter group can be reasonably characterized by its behaviour in dihedral reflection subgroups of that Coxeter group. These results were taken from our recent papers in J. Alg and PJM.
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After the seminar we will take the speaker to lunch at the Grandstand.
See the Algebra Seminar web page for information about other seminars in the series.
John Enyang John.Enyang@sydney.edu.au