Quantum Schur duality of affine type C with three parameters

TL;DR

This paper develops a three-parameter Schur duality linking affine Hecke algebras of type C with a quantum affine algebra, extending to types B, C, D at special parameters, enriching the understanding of quantum symmetries.

Contribution

It introduces a new three-parameter Schur duality for affine type C and connects it to types B, C, D at specific parameter values, expanding the algebraic framework.

Findings

Established a three-parameter Schur duality for affine type C.

Derived Schur dualities of types B, C, D at special parameter values.

Connected affine Hecke algebras with quantum affine algebras through this duality.

Abstract

We establish a three-parameter Schur duality between the affine Hecke algebra of type C and a coideal subalgebra of quantum affine $\mathfrak{sl}_n$. At the equal parameter specializations, we obtain Schur dualities of types BCD.