Multiparameter quantum Schur duality of type B

Abstract

We establish a Schur-type duality between a coideal subalgebra of the quantum group of type A and the Hecke algebra of type B with two parameters. We identify the $\imath$-canonical basis on the tensor product of the natural representation with Lusztig’s canonical basis of the type B Hecke algebra with unequal parameters associated to a weight function.