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Representation Theory

ISSN 1088-4165



Translation for finite $W$-algebras

Author: Simon M. Goodwin
Journal: Represent. Theory 15 (2011), 307-346
MSC (2010): Primary 17B10, 17B35
Published electronically: April 5, 2011
MathSciNet review: 2788896
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Abstract: 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

Received by editor(s): September 22, 2009
Received by editor(s) in revised form: June 4, 2010
Published electronically: April 5, 2011
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.