Representations of Two-Parameter Quantum Groups and Schur-Weyl Duality

Details Representations of Two-Parameter Quantum Groups and Schur-Weyl Duality Representations of Two-Parameter Quantum Groups and Schur-Weyl Duality

2001-08-06

arxiv.org/abs/math/0108038v1

Mathematics

Quantum Algebra

25 pages, AMS-TeX

Scientific paper

We determine the finite-dimensional simple modules for two-parameter quantum groups corresponding to the general linear and special linear Lie algebras gl_n and sl_n, and give a complete reducibility result. These quantum groups have a natural n-dimensional module V. We prove an analogue of Schur-Weyl duality in this setting: the centralizer algebra of the quantum group action on the k-fold tensor power of V is a quotient of a Hecke algebra for all n and is isomorphic to the Hecke algebra in case n\geq k.

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