J. Korean Math. Soc. 2003; 40(1): 1-28
Printed January 1, 2003
Copyright © The Korean Mathematical Society.
Dongho Moon
Sejong University
The Iwahori-Hecke algebra $\mathcal H_k(q^2)$ of type A acts on the $k$-fold tensor product space of the natural representation of the quantum superalgebra $\mathfrak U_q(gl(m,n))$. We show the Hecke algebra $\mathcal H_k(q^2)$ and the quantum superalgebra $\mathfrak U_q(gl(m,n))$ have commuting actions on the tensor product space, and determine the centralizer of each other. Using this result together with Gyoja's $q$-analogue of the Young symmetrizers, we construct highest weight vectors of irreducible summands of the tensor product space.
Keywords: quantum superalgebra, maximal vector, Hecke algebra, Schur-Weyl duality
MSC numbers: Primary 17B37, 20C08; Secondary 05A17
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