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

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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.
25 pages, AMS-TeX

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Quantum Algebra, Representation Theory, 17B37, 16W30, 16W35, 81R50

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http://salesiana.dossiersoluciones.com/handle/123456789/61976

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0108038
 http://arxiv.org/abs/math/0108038

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arXiv