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arXiv · 1312.2402

A class of representations of Hecke algebras II

Dean Alvis
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Abstract

Let $W$ be a Coxeter group whose proper parabolic subgroups are finite. According to Theorem~1.12 of [1], if the module of a finite $W$-digraph $\Gamma$ is isomorphic to the module of a $W$-graph over $Q$, then $\Gamma$ is acyclic. We extend this result to Coxeter groups with finite dihedral parabolic subgroups and $W$-graphs over arbitrary fields $F$ of $C$. Also, an example is provided showing the converse of this theorem is false. That is, there is an example of a finite, acyclic $W$-digraph whose module does not afford a $W$-graph.

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Dean Alvis. 2013-12-09. A class of representations of Hecke algebras II. https://arxiv.org/abs/1312.2402

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