A Class of Representations of Hecke Algebras
Vol. 11 No. 2 (2016) P.301~P.342
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.
Hecke algebra, Coxeter group, directed multigraph.
MATHEMATICAL SUBJECT CLASSIFICATION 2010
Download Full Content
Revised : 2015-05-02