Representations of Two-Parameter Quantum Groups and Schur-Weyl Duality
Quantum Algebra
2007-05-23 v1 Representation Theory
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.
Cite
@article{arxiv.math/0108038,
title = {Representations of Two-Parameter Quantum Groups and Schur-Weyl Duality},
author = {Georgia Benkart and Sarah Witherspoon},
journal= {arXiv preprint arXiv:math/0108038},
year = {2007}
}
Comments
25 pages, AMS-TeX