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

By Georgia Benkart, S. Witherspoon. 2001

77 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d4e18771c7b2f8895845e10e28d05b9a08aca9de