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G.I. Lehrer

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

    Пнд, 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.

  2. Reflection subgroups of finite and affine Weyl groups.

    Чт, 09/03/2009 - 17:38 — SomNambul
    Authors: M.J. Dyer, G.I. Lehrer
    Subjects: Group Theory
    Abstract

    We discuss the classification of reflection subgroups of finite and affine
    Weyl groups from the point of view of their root systems. A short case free
    proof is given of the well known classification of the isomorphism classes of
    reflection subgroups using completed Dynkin diagrams, for which there seems to
    be no convenient source in the literature. This is used as a basis for treating
    the affine case, where finer classifications of reflection subgroups are given,
    and combinatorial aspects of root systems are shown to appear.

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