A class of representations of Hecke algebras

Abstract

A type of directed multigraph called a W-digraph is introduced to model the structure of certain representations of Hecke algebras, including those constructed by Lusztig and Vogan from involutions in a Weyl group. Building on results of Lusztig, a complete characterization of W-digraphs is given in terms of subdigraphs for dihedral parabolic subgroups. Graph-theoretic properties of W-digraphs are established including, under certain assumptions, acyclicity. In case the Coxeter system is finite, a bound on the number of vertices of a connected W-digraph is obtained, and a graph-theoretic version of the usual duality operation is obtained.

revised version, currently under review

References in corpus (2)

• Hecke algebras and involutions in Weyl groups
• A bar operator for involutions in a Coxeter group

Cited by in corpus (2)

• An extension of a theorem and errata for "A Class of Representations of Hecke Algebras"
• A class of representations of Hecke algebras II