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 II: Groups of rank five and six
Optional Fields
Coxeter group Descent algebra Orlik-Solomon algebra REFLECTION GROUPS
In recent papers we have refined a conjecture of Lehrer and Solomon expressing the character of a finite Coxeter group W acting on the graded components of its Orlik-Solomon algebra as a sum of characters induced from linear characters of centralizers of elements of W. The refined conjecture relates the character above to a decomposition of the regular character of W related to Solomon's descent algebra of W. The refined conjecture has been proved for symmetric and dihedral groups, as well as for finite Coxeter groups of rank three and four. In this paper, we prove the conjecture for finite Coxeter groups of rank five and six. The techniques developed and implemented in this paper provide previously unknown decompositions of the regular and Orlik-Solomon characters of the groups considered. (C) 2012 Elsevier Inc. All rights reserved.
DOI 10.1016/j.jalgebra.2012.11.047
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