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 Representation Theory
Representation Theory
ISSN 1088-4165

     

Harish-Chandra bimodules for quantized Slodowy slices

Author(s): Victor Ginzburg
Journal: Represent. Theory 13 (2009), 236-271.
MSC (2000): Primary 81R10
Posted: June 30, 2009
MathSciNet review: 2515934
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Abstract | References | Similar articles | Additional information

Abstract: The Slodowy slice is an especially nice slice to a given nilpotent conjugacy class in a semisimple Lie algebra. Premet introduced noncommutative quantizations of the Poisson algebra of polynomial functions on the Slodowy slice.

In this paper, we define and study Harish-Chandra bimodules over Premet's algebras. We apply the technique of Harish-Chandra bimodules to prove a conjecture of Premet concerning primitive ideals, to define projective functors, and to construct ``noncommutative resolutions'' of Slodowy slices via translation functors.

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Additional Information:

Victor Ginzburg
Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
Email: ginzburg@math.uchicago.edu

DOI: 10.1090/S1088-4165-09-00355-0
PII: S 1088-4165(09)00355-0
Received by editor(s): November 10, 2008
Received by editor(s) in revised form: March 31, 2009
Posted: June 30, 2009
Dedicated: Dedicated to the memory of Peter Slodowy
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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