Quantum supersymmetric pairs and $ı$Schur duality of type AIII

Abstract

We construct quantum supersymmetric pairs $(\mathbf{U},{\mathbf{U}}^{ı})$ of type AIII and elucidate their fundamental properties. An $ı$Schur duality between the $ı$quantum supergroup ${\mathbf{U}}^{ı}$ and the Hecke algebra of type B acting on a tensor space is established, providing a super generalization of the $ı$Schur duality of type AIII. Additionally, we construct a (quasi) $K$-matrix for arbitrary parameters, which facilitates the realization of the Hecke algebra action on the tensor space.

arXiv comment43 pages; v2, references added; v3, major modifications to improve readablity