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Harish-Chandra bimodules for quantized Slodowy slices


Author: Victor Ginzburg
Journal: Represent. Theory 13 (2009), 236-271
MSC (2000): Primary 81R10
DOI: https://doi.org/10.1090/S1088-4165-09-00355-0
Published electronically: June 30, 2009
MathSciNet review: 2515934
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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: https://doi.org/10.1090/S1088-4165-09-00355-0
Received by editor(s): November 10, 2008
Received by editor(s) in revised form: March 31, 2009
Published electronically: June 30, 2009
Dedicated: Dedicated to the memory of Peter Slodowy
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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