A class of representations of Hecke algebras II

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.

This paper is an extension of arXiv:1306.4821, which has appeared in Bull. Inst. Math. Acad. Sinica (NS), 11(2016), No. 2, 301--342

References in corpus (1)

• A class of representations of Hecke algebras