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Stephen Griffeth

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

    Чт, 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. Catalan numbers for complex reflection groups.

    Ср, 12/09/2009 - 16:01 — SomNambul
    Authors: Iain Gordon, Stephen Griffeth
    Subjects: Combinatorics
    Abstract

    We construct (q,t)-Catalan polynomials and q-Fuss-Catalan polynomials for any
    irreducible complex reflection group W. The two main ingredients in this
    construction are Rouquier's formulation of shift functors for the rational
    Cherednik algebras of W, and Opdam's analysis of permutations of the
    irreducible representations of W arising from the Knizhnik-Zamolodchikov
    connection.

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