Browsing by Author "Douglass, J. Matthew"

Now showing 1 - 3 of 3
  • Thumbnail Image
    Item
    Coxeter arrangements and Solomon's descent algebra
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Douglass, J. Matthew; Pfeiffer, Götz; Röhrle, Gerhard
    In our recent paper [3], 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 representations of centralizers, one for each conjugacy class of elements of W, and gave a uniform proof of this claim for symmetric groups. In this note we outline an inductive approach to our conjecture. As an application of this method, we prove the inductive version of the conjecture for nite Coxeter groups of rank up to 2.
  • Thumbnail Image
    Item
    On reflection subgroups of finite Coxeter groups
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Douglass, J. Matthew; Pfeiffer, Götz; Röhrle, Gerhard
    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 Coxeter elements to be injective, up to conjugacy.
  • Thumbnail Image
    Item
    On the Invariants of the Cohomology of Complements of Coxeter Arrangements
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2018) Douglass, J. Matthew; Pfeiffer, Götz; Röhrle, Gerhard
    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 basis of the space of W-invariants in this cohomology ring.