Computations for Coxeter arrangements and Solomon's descent algebra III:   Groups of rank seven and eight
  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. 
Marcus Bishop and J. Matthew Douglass and Goetz Pfeiffer and Gerhard   Roehrle
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