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arXiv · 1306.4821

A class of representations of Hecke algebras

Dean Alvis
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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.

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Dean Alvis. 2013-06-20. A class of representations of Hecke algebras. https://arxiv.org/abs/1306.4821

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