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Charles Dunkl

  1. Generalized Jack polynomials and the representation theory of rational Cherednik algebras.

    Thu, 02/25/2010 - 16:01 — SomNambul
    Authors: Charles Dunkl, Stephen Griffeth
    Subjects: Representation Theory
    Abstract

    We apply the Dunkl-Opdam operators and generalized Jack polynomials to study
    category O for the rational Cherednik algebra of type G(r,1,n). We determine
    the set of aspherical values, and answer a question of Iain Gordon on the
    ordering of category O.

  2. Volume of the set of unistochastic matrices of order 3 and the mean Jarlskog invariant.

    Wed, 09/02/2009 - 12:02 — SomNambul
    Authors: Charles Dunkl, Karol Zyczkowski
    Subjects: Mathematical Physics
    Abstract

    A bistochastic matrix B of size N is called unistochastic if there exists a
    unitary U such that B_ij=|U_{ij}|^{2} for i,j=1,...,N. The set U_3 of all
    unistochastic matrices of order N=3 forms a proper subset of the Birkhoff
    polytope, which contains all bistochastic (doubly stochastic) matrices. We
    compute the volume of the set U_3 with respect to the flat (Lebesgue) measure
    and analytically evaluate the mean entropy of an unistochastic matrix of this
    order.

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