Publication

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

Bishop, Marcus
; 
Douglass, J. Matthew
; 
Pfeiffer, Götz
; 
Röhrle, Gerhard
Thumbnail Image
Files
Thumbnail Image
rank7and8.pdf
Adobe PDF, 342.39 KB
Repository DOI
Publication Date
2014-11-06
Keywords
Coxeter group, Orlik-Solomon algebra, Descent algebra, HYPERPLANE COMPLEMENTS, REFLECTION GROUPS, WEYL GROUPS, COMBINATORICS, Algebra, Mathematics
Type
Article
Downloads
Show all metadata
Citation
Bishop, Marcus, Matthew Douglass, J., Pfeiffer, Götz, & Röhrle, Gerhard. (2015). Computations for Coxeter arrangements and Solomon's descent algebra III: Groups of rank seven and eight. Journal of Algebra, 423(Supplement C), 1213-1232. doi: https://doi.org/10.1016/j.jalgebra.2014.10.025
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 p-th 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. (C) 2014 Elsevier Inc. All rights reserved.
Funder
|~|
Publisher
Elsevier
Publisher DOI
10.1016/j.jalgebra.2014.10.025
Rights
Attribution-NonCommercial-NoDerivs 3.0 Ireland
cbn
Collections
Mathematics (Scholarly Articles)