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• W1880661644 abstract "We introduce a new family of superalgebras, the quantum walled Brauer-Clifford superalgebras ${mathsf {BC}}_{r,s}(q)$. The superalgebra ${mathsf {BC}}_{r,s}(q)$ is a quantum deformation of the walled Brauer-Clifford superalgebra ${mathsf {BC}}_{r,s}$ and a super version of the quantum walled Brauer algebra. We prove that ${mathsf {BC}}_{r,s}(q)$ is the centralizer superalgebra of the action of ${mathfrak U}_{q}({mathfrak q}(n))$ on the mixed tensor space $mathbf{V}_{q}^{r,s}=mathbf{V}_{q}^{otimes r} otimes (mathbf{V}_q^*)^{otimes s}$ when $n ge r+s$, where ${mathbf V}_{q}=mathbb{C}(q)^{(n|n)}$ is the natural representation of the quantum enveloping superalgebra ${mathfrak U}_{q}({mathfrak q}(n))$ and $mathbf{V}_q^*$ is its dual space. We also provide a diagrammatic realization of ${mathsf {BC}}_{r,s}(q)$ as the $(r,s)$-bead tangle algebra ${mathsf {BT}}_{r,s}(q)$. Finally, we define the notion of $q$-Schur superalgebras of type $mathsf{Q}$ and establish their basic properties." @default.
• W1880661644 created "2016-06-24" @default.
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• W1880661644 date "2014-04-02" @default.
• W1880661644 modified "2023-10-18" @default.
• W1880661644 title "Quantum walled Brauer-Clifford superalgebras" @default.
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