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Jae-Hoon Kwon

  1. A plactic algebra of extremal weight crystals and the Cauchy identity for Schur operators.

    Ср, 07/07/2010 - 15:01 — SomNambul
    Authors: Jae-Hoon Kwon
    Subjects: Representation Theory
    Abstract

    We give a new bijective interpretation of the Cauchy identity for Schur
    operators which is a commutation relation between two formal power series with
    operator coefficients. We introduce a plactic algebra associated with the
    Kashiwara's extremal weight crystals over the Kac-Moody algebra of type
    $A_{+\infty}$, and construct a Knuth type correspondence preserving the plactic
    relations.

  2. Crystal bases of modified quantum groups and RSK correspondence.

    Втр, 02/09/2010 - 16:01 — SomNambul
    Authors: Jae-Hoon Kwon
    Subjects: Representation Theory
    Abstract

    The crystal base of the modified quantum group of type $A_{+\infty}$ is
    realized as a set of integral bimatrices. It is obtained by describing
    explicitly the tensor product of a highest weight crystal and a lowest weight
    crystal, and then its limit using a tableaux model of extremal weight crystals.
    This realization induces a bicrystal structure of the crystal base of the
    modified quantum group and hence its Peter-Weyl type decomposition in a purely
    combinatorial way generalizing the classical RSK correspondence.

  3. Crystal duality and Littlewood-Richardson rule of extremal weight crystals.

    Втр, 09/08/2009 - 12:16 — SomNambul
    Authors: Jae-Hoon Kwon
    Subjects: Quantum Algebra
    Abstract

    We consider a category of $\gl_\infty$-crystals, whose object is a disjoint
    union of extremal weight crystals with bounded non-negative level and finite
    multiplicity for each connected component. We show that it is a monoidal
    category under tensor product of crystals and the associated Grothendieck ring
    is anti-isomorphic to an Ore extension of the character ring of integrable
    lowest $\gl_\infty$-modules with respect to derivations shifting the
    fundamental weight characters.

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