Now showing items 1-7 of 7

    • Cohomology of Coxeter arrangements and Solomon's descent algebra 

      Douglass, J. Matthew; Pfeiffer, Götz; Röhrle, Gerhard (American Mathematical Society, 2014-06-19)
      We refine a conjecture by Lehrer and Solomon on the structure of the Orlik-Solomon algebra of a finite Coxeter group W and relate it to the descent algebra of W. As a result, we claim that both the group algebra of W and ...
    • Computations for Coxeter arrangements and Solomon's descent algebra II: Groups of rank five and six 

      Bishop, Marcus; Douglass, J. Matthew; Pfeiffer, Götz; Röhrle, Gerhard (Elsevier, 2013-01-08)
      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 ...
    • 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 (Elsevier, 2014-11-06)
      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 ...
    • Computations for Coxeter arrangements and Solomon's descent algebra: Groups of rank three and four 

      Bishop, Marcus; Douglass, J. Matthew; Pfeiffer, Götz; Röhrle, Gerhard (Elsevier, 2012-06-03)
      In recent papers we have refined a conjecture of Lehrer and Solomon expressing the characters of a finite Coxeter group W afforded by the homogeneous components of its Orlik-Solomon algebra as sums of characters induced ...
    • An inductive approach to Coxeter arrangements and Solomon's descent algebra 

      Dolan, J. Matthew; Pfeiffer, Götz; Röhrle, Gerhard (Springer Verlag, 2012-07-20)
      In our recent paper (Douglass et al. arXiv: 1101.2075 (2011)), we claimed that both the group algebra of a finite Coxeter group W as well as the Orlik-Solomon algebra of W can be decomposed into a sum of induced one-dimensional ...
    • On reflection subgroups of finite Coxeter groups 

      Douglass, J. Matthew; Pfeiffer, Götz; Röhrle, Gerhard (Taylor & Francis, 2013-06-14)
      Let W be a finite Coxeter group. We classify the reflection subgroups of W up to conjugacy and give necessary and sufficient conditions for the map that assigns to a reflection subgroup R of W the conjugacy class of its ...
    • On the invariants of the cohomology of complements of Coxeter arrangements 

      Douglass, J. Matthew; Pfeiffer, Götz; Röhrle, Gerhard (Elsevier, 2019-05-24)
      We refine Brieskorn's study of the cohomology of the complement of the reflection arrangement of a finite Coxeter group W. As a result we complete the verification of a conjecture by Felder and Veselov that gives an explicit ...