Computations for Coxeter arrangements and Solomon's descent algebra III: Groups of rank seven and eight
Douglass, J. Matthew
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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
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.