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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Quantum algebras and symplectic reflection algebras for wreath products
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by Nicolas Guay PDF
Represent. Theory 14 (2010), 148-200 Request permission


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
  • Email:
  • Received by editor(s): October 19, 2007
  • Received by editor(s) in revised form: September 29, 2009
  • Published electronically: February 9, 2010
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 14 (2010), 148-200
  • MSC (2010): Primary 17B37; Secondary 20C08
  • DOI:
  • MathSciNet review: 2593918