| In this article,we first introduce a so-called duplex Hecke algebras of type B.This notion originates from the degenerate duplex Hecke algebra arising from the course of study of enhanced reductive groups,its Levi subgorups and related Schur-Weyl duality,extending the duplex Hecke algebra of type A arising from the related q-Schur-Weyl duality of Levi-type.The approach to duality of type A cannot apply directly to type B.We will study the natural presetation of duplex Hecke algebras of type B on certain tensor spaces and establish a Levi-type q-Schur-Weyl duality of type B,which reveals the double centralizer property between such a duplex Hecke algebra and Levi-type ι quantum groups. |
