Celebratio Mathematica — Benkart

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G. Benkart, N. Guay, J. H. Jung, S.-J. Kang, and S. Wilcox: “Quantum walled Brauer–Clifford superalgebras,” J. Algebra 454 (May 2016), pp. 433–474. MR 3473434 Zbl 1342.17002 ArXiv 1404.0443 article

We introduce a new family of superalgebras, the quantum walled Brauer–Clifford superalgebras \( \mathbf{BC}_{r,s}(q) \). The superalgebra \( \mathbf{BC}_{r,s}(q) \) is a quantum deformation of the walled Brauer–Clifford superalgebra \( \mathbf{BC}_{r,s} \) and a super version of the quantum walled Brauer algebra. We prove that \( \mathbf{BC}_{r,s}(q) \) 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 \( n \geq r+s \), 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 \( \mathbf{BC}_{r,s}(q) \) as the \( (r,s) \)-bead tangle algebra \( \mathbf{BT}_{r,s}(q) \). Finally, we define the notion of \( q \)-Schur superalgebras of type \( \mathbf{Q} \) and establish their basic properties.

Stewart Wilcox	Related
Nicolas Guay	Related
Ji Hye Jung	Related
Seok-Jin Kang	Related