Computations for Coxeter arrangements and Solomon's descent algebra III: Groups of rank seven and eight

2014/03/25 by Marcus Bishop, J. Matthew Douglass, Bishop, Marcus +4
Computer Science · Mathematics · #20C15 #20C40 #20F55 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Coding theory and cryptography #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1403.6227

openalex publication_date 2014/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we extend the computations in parts I and II of this series of papers and complete the proof of a conjecture of Lehrer and Solomon expressing the character of a finite Coxeter group W acting on the pth graded component of its Orlik-Solomon algebra as a sum of characters induced from linear characters of centralizers of elements of W for groups of rank seven and eight. For classical Coxeter groups, these characters are given using a formula that is expected to hold in all ranks.

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