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Representation Theory
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
Email: goodwin@for.mat.bham.ac.uk

DOI: http://dx.doi.org/10.1090/S1088-4165-2011-00388-5
PII: S 1088-4165(2011)00388-5
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.