Quantum walled Brauer-Clifford superalgebras

JOURNAL OF ALGEBRA

卷:454

Article

Benkart, Georgia¹  Guay, Nicolas²  Jung, Ji Hye^3,4,5 

[1] Univ Wisconsin, Dept Math, Madison, WI 53706 USA

[2] Univ Alberta, Dept Math & Stat Sci, CAB 632, Edmonton, AB T6G 2G1, Canada

[3] Seoul Natl Univ, Dept Math Sci, Seoul 151747, South Korea

[4] Seoul Natl Univ, Res Inst Math, Seoul 151747, South Korea

[5] Univ Paris 06, CNRS, Inst Math Jussieu Paris Rive Gauche, Univ Paris 07, F-75205 Paris 13, France

关键词: Quantum walled Brauer-Clifford superalgebra;    Queer Lie superalgebra;    Centralizer algebra;    Bead tangle algebra;    q-Schur superalgebra;   

DOI  :  10.1016/j.jalgebra.2015.04.038

来源: Elsevier

【 摘 要 】

We introduce a new family of superalgebras, the quantum walled Brauer-Clifford superalgebras BCr,s (q). The superalgebra BCr,s (q) is a quantum deformation of the walled Brauer-Clifford superalgebra BCr,s and a super version of the quantum walled Brauer algebra. We prove that BCr,s (q) is the centralizer superalgebra of the action of U-q (q(n)) on the mixed tensor space V-q(r,s) = V-q(circle times r) circle times (V-q*)(circle times s) when n >= r + s, where V-q = C(q)((n\n)) is the natural representation of the quantum enveloping superalgebra U-q(q(n)) and V-q* is its dual space. We also provide a diagrammatic realization of BCr,s (q) as the (r, s)-bead tangle algebra BTr,s (q). Finally, we define the notion of q-Schur superalgebras of type Q and establish their basic properties. (C) 2015 Published by Elsevier Inc.

【 授权许可】

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