Highest weight vectors of irreducible representations of the quantum superalgebra U_q(gl(m,n))

Details Highest weight vectors of irreducible representations of the quantum superalgebra U_q(gl(m,n)) Highest weight vectors of irreducible representations of the quantum superalgebra U_q(gl(m,n))

2001-05-25

arxiv.org/abs/math/0105204v1

Mathematics

Quantum Algebra

Scientific paper

The Iwahori-Hecke algebra of type A acts on tensor product space of the natural representation of the quantum superalgebra U_q(gl(m,n)). We show this action of the Hecke algebra and the action of U_q(gl(m,n)) on the same space determine commuting actions of each other. Together with this result and Gyoja's q-analogue of the Young symmetrizer, we construct a highest weight vector of each irreducible summmand of the tensor product space.

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