Peer-Reviewed Journal Details
Mandatory Fields
Bishop, M,Douglass, JM,Pfeiffer, G,Rohrle, G
Journal Of Algebra
Computations for Coxeter arrangements and Solomon's descent algebra III: Groups of rank seven and eight
WOS: 1 ()
Optional Fields
Coxeter group Orlik-Solomon algebra Descent algebra HYPERPLANE COMPLEMENTS
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.
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