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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Quantum algebras and symplectic reflection algebras for wreath products
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by Nicolas Guay
Represent. Theory 14 (2010), 148-200
Published electronically: February 9, 2010


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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Bibliographic 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