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Representation Theory

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Quantum algebras and symplectic reflection algebras for wreath products

Author: Nicolas Guay
Journal: Represent. Theory 14 (2010), 148-200
MSC (2010): Primary 17B37; Secondary 20C08
Published electronically: February 9, 2010
MathSciNet review: 2593918
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Abstract: To a finite subgroup $ \Gamma$ of $ SL_2(\mathbb{C})$, we associate a new family of quantum algebras which are related to symplectic reflection algebras for wreath products $ S_l\wr\Gamma$ via a functor of Schur-Weyl type. We explain that they are deformations of matrix algebras over rank-one symplectic reflection algebras for $ \Gamma$ and construct for them a PBW basis. When $ \Gamma$ is a cyclic group, we are able to give more information about their structure and to relate them to Yangians.

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Additional Information

Nicolas Guay
Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, CAB 632, Edmonton, Alberta T6G 2G1, Canada

Received by editor(s): October 19, 2007
Received by editor(s) in revised form: September 29, 2009
Published electronically: February 9, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.