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

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dc.creatorBenkart, Georgia
dc.creatorWitherspoon, Sarah
dc.date2001-08-06
dc.date.accessioned2026-07-07T04:42:53Z
dc.date.available2026-07-07T04:42:53Z
dc.descriptionWe 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.
dc.description25 pages, AMS-TeX
dc.identifierhttps://arxiv.org/abs/math/0108038
dc.identifierhttp://arxiv.org/abs/math/0108038
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61976
dc.subjectQuantum Algebra
dc.subjectRepresentation Theory
dc.subject17B37, 16W30, 16W35, 81R50
dc.titleRepresentations of Two-Parameter Quantum Groups and Schur-Weyl Duality
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