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Catharina Stroppel

  1. Quiver Schur algebras and q-Fock space.

    Fri, 10/07/2011 - 15:01 — SomNambul
    Authors: Ben Webster, Catharina Stroppel
    Subjects: Rings and Algebras
    Abstract

    We develop a graded version of the theory of cyclotomic q-Schur algebras, in
    the spirit of the work of Brundan-Kleshchev on Hecke algebras and of Ariki on
    q-Schur algebras. As an application, we identify the coefficients of the
    canonical basis on a higher level Fock space with q-analogues of the
    decomposition numbers of cyclotomic q-Schur algebras.

  2. Gradings on walled Brauer algebras and Khovanov's arc algebra.

    Thu, 07/07/2011 - 15:01 — SomNambul
    Authors: Catharina Stroppel, Jonathan Brundan
    Subjects: Representation Theory
    Abstract

    We introduce some graded versions of the walled Brauer algebra, working over
    a field of characteristic zero. This allows us to prove that the walled Brauer
    algebra is Morita equivalent to an idempotent truncation of a certain infinite
    dimensional version of Khovanov's arc algebra, as suggested by recent work of
    Cox and De Visscher. We deduce that the walled Brauer algebra is Koszul
    whenever its defining parameter is non-zero.

  3. Cuspidal $\mathfrak{sl}_n$-modules and deformations of certain Brauer tree algebras.

    Mon, 01/18/2010 - 16:01 — SomNambul
    Authors: Catharina Stroppel, Volodymyr Mazorchuk
    Subjects: Representation Theory
    Abstract

    We show that the algebras describing blocks of the category of cuspidal
    weight (respectively generalized weight) $\mathfrak{sl}_n$-modules are
    one-parameter (respectively multi-parameter) deformations of certain Brauer
    tree algebras. We explicitly determine these deformations both graded and
    ungraded. The algebras we deform also appear as special centralizer subalgebras
    of Temperley-Lieb algebras or as generalized Khovanov algebras.

  4. The sl(n)-WZNW Fusion Ring: a combinatorial construction and a realisation as quotient of quantum cohomology.

    Tue, 09/15/2009 - 11:27 — SomNambul
    Authors: Christian Korff, Catharina Stroppel
    Subjects: Representation Theory
    Abstract

    A simple, combinatorial construction of the sl(n)-WZNW fusion ring, also
    known as Verlinde algebra, is given. As a byproduct of the construction one
    obtains an isomorphism between the fusion ring and a particular quotient of the
    small quantum cohomology ring of the Grassmannian Gr(k,k+n). We explain how our
    approach naturally fits into known combinatorial descriptions of the quantum
    cohomology ring, by establishing what one could call a
    `Boson-Fermion-correspondence' between the two rings.

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