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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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Harish-Chandra bimodules for quantized Slodowy slices
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by Victor Ginzburg PDF
Represent. Theory 13 (2009), 236-271 Request permission


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:
  • 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
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 13 (2009), 236-271
  • MSC (2000): Primary 81R10
  • DOI:
  • MathSciNet review: 2515934