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

2001/08/06 by Georgia Benkart, Benkart, Georgia, Sarah Witherspoon +1 · 1 citation
Mathematics · #16W30 #16W35 #17B37 #81R50 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:16W30 #msc:16W35 #msc:17B37 #msc:81R50

paper · pdf · doi:10.48550/arxiv.math/0108038

25 pages, AMS-TeX

arxiv created 2001/08/06 · arxiv updated 2009/11/30

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≥ k.

Cited by

• Simple Modules and PI Structure of the Two-Parameter Quantized Algebra U⁺_r,s(B₂)

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