Iquantum Groups Of Type AⅢ And ISchur Duality

In 1986,Jimbo established a quantum analog of the classical Schur-Weyl duality.Let Uq(gIn)denote the quantum group of gIn,and(Gd)the Hecke algebra of type A.He discovered that the actions of Uq(gIn)and(Gd)on tensor space V(?)d satisfy the double centralizer property.It is known that the quantum groups of type B and the Hecke algebra H(Wd)of type Bd do not form the double centralizer.In 2018,Bao and Wang discovered the double centralizer property between the iquantum group U’ and H(Wd).This is called iSchur-Weyl duality.Hence,there should exist a deep connection between the representation theory of U’ and that of H(Wd).This article will study the classification of irreducible classical weight module of U’=Uqi(gI2r+2)with two parameters and the irreducible decomposition of V(?)d as U’-H(Wd)bimodule will be given.