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

Abstract

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

References in corpus (1)

• Two-Parameter Quantum Groups and Drinfel'd Doubles

Cited by in corpus (10)

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• Two dualities: Markov and Schur-Weyl
• On fusion procedure for the two-parameter quantum algebra in type A
• Two-Parameter Quantum Groups and Drinfel'd Doubles
• Derivations of the Positive Part of the Two-parameter Quantum Group of type $G_2$
• $RLL$-Realization and Its Hopf Superalgebra Structure of $U_{p,q}(\widehat{\mathfrak{gl}(m|n))}$