A class of representations of Hecke algebras II

2013/12/09 by Dean Alvis, Alvis, Dean
Mathematics · #20C08 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1312.2402

openalex publication_date 2013/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Γ is isomorphic to the module of a W-graph over Q, then Γ 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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