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A Class of Representations of Hecke Algebras
by Dean Alvis  

Vol. 11 No. 2 (2016) P.301~P.342

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. In addition, results are obtained relating graph-theoretic properties of W- digraphs (acyclicity, existence of sources or sinks, connectedness) to the structure of the corresponding H-module or its character.


KEYWORDS
Hecke algebra, Coxeter group, directed multigraph.

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 20C08.

MILESTONES

Received: 2014-12-19
Revised : 2015-05-02
Accepted: 2015-05-01


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