A Reduction theorem for the W-graph decomposition conjecture

2017/07/10 by Johannes Hahn, Hahn, Johannes
Computer Science · Mathematics · #16G30 #20C08 #20F55 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1707.02952

openalex publication_date 2017/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let W be a finite Coxeter group and Ω be its W-graph algebra as defined by Gyoja. The author's previous paper \citehahn2016wgraphs considered this algebra in some detail, proposed, and proved in some small cases the W-graph decomposition conjecture. The purpose of the current paper is to prove a reduction theorem for (a slightly stronger version of) that conjecture to indecomposable Coxeter groups in the sense that the conjecture is true for W=W₁× W₂ if it holds for W₁ and W₂.

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