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Goetz Pfeiffer

  1. Computations for Coxeter arrangements and Solomon's descent algebra: Groups of rank three and four.

    Tue, 10/04/2011 - 15:01 — SomNambul
    Authors: Gerhard Roehrle, J. Matthew Douglass, Goetz Pfeiffer, Marcus Bishop
    Subjects: Representation Theory
    Abstract

    In recent papers we have refined a conjecture of Lehrer and Solomon
    expressing the character of the representation of a finite Coxeter group $W$ on
    the $p$th graded piece of its Orlik-Solomon algebra as a sum of characters
    induced from linear characters of centralizers of elements of $W$. Our refined
    conjecture relates the character of $W$ on the $p$th graded piece of its
    Orlik-Solomon algebra with the descent algebra of $W$.

  2. Coxeter arrangements and Solomon's descent algebra.

    Wed, 01/12/2011 - 16:01 — SomNambul
    Authors: Gerhard Roehrle, J. Matthew Douglass, Goetz Pfeiffer
    Subjects: Representation Theory
    Abstract

    We refine a conjecture by Lehrer and Solomon on the structure of the
    Orlik--Solomon algebra of a finite Coxeter group $W$, related it to the descent
    algebra of $W$ and prove the conjecture for symmetric groups.

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