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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.


Translation for finite $W$-algebras
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by Simon M. Goodwin
Represent. Theory 15 (2011), 307-346
Published electronically: April 5, 2011


A finite $W$-algebra $U(\mathfrak {g},e)$ is a certain finitely generated algebra that can be viewed as the enveloping algebra of the Slodowy slice to the adjoint orbit of a nilpotent element $e$ of a complex reductive Lie algebra $\mathfrak {g}$. It is possible to give the tensor product of a $U(\mathfrak {g},e)$-module with a finite dimensional $U(\mathfrak {g})$-module the structure of a $U(\mathfrak {g},e)$-module; we refer to such tensor products as translations. In this paper, we present a number of fundamental properties of these translations, which are expected to be of importance in understanding the representation theory of $U(\mathfrak {g},e)$.
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Bibliographic Information
  • Simon M. Goodwin
  • Affiliation: School of Mathematics, University of Birmingham, Birmingham, B15 2TT, United Kingdom
  • MR Author ID: 734259
  • Email:
  • Received by editor(s): September 22, 2009
  • Received by editor(s) in revised form: June 4, 2010
  • Published electronically: April 5, 2011
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 15 (2011), 307-346
  • MSC (2010): Primary 17B10, 17B35
  • DOI:
  • MathSciNet review: 2788896