An extension of a theorem and errata for "A Class of Representations of\n Hecke Algebras"

2021/06/30 by Dean Alvis, Alvis, Dean
Computer Science · Mathematics · #20C08 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2107.00084

openalex publication_date 2021/06/30 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

By Theorem~1.12 of the paper "A Class of Representations of Hecke Algebras",\nif W is a Coxeter group whose proper parabolic subgroups are finite, and if\nthe module of a finite W-digraph \Γ is isomorphic to the module of a\nW-graph, then \Γ must be acyclic. Here we extend this result to Coxeter\ngroups with finite dihedral parabolic subgroups and W-graphs with arbitrary\nscalar edge labels. Also, errata for the paper are listed in the last section.\n

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• A Construction of Coxeter Group Representations (II)
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• A classification of commutative parabolic Hecke algebras
• A Reduction theorem for the W-graph decomposition conjecture