CU Algebraic Lie Theory Seminar

A tableaux correspondence for commutation classes

Hugh Denoncourt, CU

Abstract

Commutation classes are equivalence classes on words that are equivalent by a sequence of commutation relations; that is to say, relations of the form xy=yx. They provide a framework for studying the combinatorial properties of reduced expressions for Coxeter group elements (or for studying the associated roots). We show that the commutation classes for a reduced word of a permutation are in correspondence with certain tableaux and demonstrate interesting features of this correspondence.