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Jun Hu

  1. BMW algebra, quantized coordinate algebra and type C Schur--Weyl duality.

    Wed, 11/18/2009 - 16:01 — SomNambul
    Authors: Jun Hu
    Subjects: Quantum Algebra
    Abstract

    We prove an integral version of the Schur--Weyl duality between the
    specialized Birman--Murakami--Wenzl algebra $B_n(-q^{2m+1},q)$ and the quantum
    algebra associated to the symplectic Lie algebra sp_{2m}. In particular, we
    deduce that this Schur--Weyl duality holds over arbitrary (commutative) ground
    rings, which answers a question of Lehrer and Zhang [Strongly multiplicity free
    modules for Lie algebras and quantum groups, J. Algebra (1) 306 (2006),
    138--174] in the symplectic case.

  2. Dual partially harmonic tensors and Brauer-Schur-Weyl duality.

    Tue, 08/18/2009 - 11:53 — SomNambul
    Authors: Jun Hu
    Subjects: Representation Theory
    Abstract

    We study the Brauer-Schur-Weyl duality between the quotient
    $\bb_n(-2m)/\bb_n^{(f)}$ of the Brauer algebra $\bb_n(-2m)$ and the symplectic
    group $Sp(V)$ on the space $\mathcal{HT}_n^{\otimes f}$ of partially harmonic
    tensors of valence $f$ in $V^{\otimes n}$, where $\bb_n^{(f)}$ is the two-sided
    ideal generated by $e_1e_3... e_{2f-1}$ and $1\leq f\leq [n/2]$.

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