A class of representations of Hecke algebras II

Dean Alvis

Published 2013-12-09, updated 2014-06-29Version 7

This paper is a continuation of [1], in which the notion of W-digraph was introduced to model the structure of certain representations of Hecke algebras, including those constructed by Lusztig from twisted involutions in the underlying Coxeter group in [4]. Here graph-theoretic properties of W-digraphs are established including, under certain assumptions, acyclicity. When the Coxeter system is finite, a bound on the number of vertices of a connected W-digraph is obtained, and a graph operation is considered that induces the usual duality operation on the level of characters.