Highest weight vectors of irreducible representations of the quantum superalgebra $\uq\left(gl(m,n) \right)$

Abstract

The Iwahori-Hecke algebra hec of type A acts on the k-foldtensor product space of the natural representation of the quantumsuperalgebra uq(gl(m,n)). We show the Hecke algebra hec andthe quantum superalgebra uq(gl(m,n)) have commuting actions onthe tensor product space, and determine the centralizer of eachother. Using this result together with Gyoja's q-analogue of theYoung symmetrizers, we construct highest weight vectors ofirreducible summands of the tensor product space.