Browsing by Author "Pfeiffer, Götz"

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    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.
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    An inductive approach to 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.
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    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.
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    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.
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    The Varchenko determinant of a Coxeter arrangement
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2017) Pfeiffer, Götz; Randriamaro, Hery
    The Varchenko determinant is the determinant of a matrix defined from an arrangement of hyperplanes. Varchenko proved that this determinant has a beautiful factorization. It is, however, not possible to use this factorization to compute a Varchenko determinant from a certain level of complexity. Precisely at this point, we provide an explicit formula of this determinant for the hyperplane arrangements associated to the finite Coxeter groups. The intersections of hyperplanes with the chambers of such arrangements have nice properties which play a central role for the calculation of their relating determinants.