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R.B. Zhang

  1. Generalised Jantzen filtration of Lie superalgebras I.

    Fri, 01/08/2010 - 16:01 — SomNambul
    Authors: Yucai Su, R.B. Zhang
    Subjects: Representation Theory
    Abstract

    A Jantzen type filtration for generalised Varma modules of Lie superalgebras
    is introduced. In the case of type I Lie superalgebras, it is shown that the
    generalised Jantzen filtration for any Kac module is the unique Loewy
    filtration, and the decomposition numbers of the layers of the filtration are
    determined by the coefficients of inverse Kazhdan-Lusztig polynomials.
    Furthermore, the length of the Jantzen filtration for any Kac module is
    determined explicitly in terms of the degree of atypicality of the highest
    weight.

  2. Quantum group actions on rings and equivariant K-theory.

    Mon, 12/21/2009 - 16:01 — SomNambul
    Authors: G.I. Lehrer, R.B. Zhang
    Subjects: Quantum Algebra
    Abstract

    Let $\Uq$ be a quantum group. Regarding a (noncommutative) space with
    $\Uq$-symmetry as a $\Uq$-module algebra $A$, we may think of equivariant
    vector bundles on $A$ as projective $A$-modules with compatible $\Uq$-action.
    We construct an equivariant K-theory of such quantum vector bundles using
    Quillen's exact categories, and provide means for its compution. The
    equivariant K-groups of quantum homogeneous spaces and quantum symmetric
    algebras of classical type are computed.

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