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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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Translation for finite $W$-algebras
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by Simon M. Goodwin PDF
Represent. Theory 15 (2011), 307-346 Request permission


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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Additional 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