A class of representations of Hecke algebras II

Dean Alvis

A class of representations of Hecke algebras II

Representation Theory 2021-10-28 v8

Authors: Dean Alvis

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.

Keywords

hecke algebras coxeter groups w-graphs w-digraphs representations acyclic graphs parabolic subgroups

Cite

@article{arxiv.1312.2402,
  title  = {A class of representations of Hecke algebras II},
  author = {Dean Alvis},
  journal= {arXiv preprint arXiv:1312.2402},
  year   = {2021}
}

Comments

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

A class of representations of Hecke algebras II

Abstract

Keywords

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