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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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On the equivariant K-theory of the nilpotent cone in the general linear group
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by Pramod N. Achar PDF
Represent. Theory 8 (2004), 180-211 Request permission

Corrigendum: Represent. Theory 20 (2016), 414-418.

Abstract:

Let $G$ be a simple complex algebraic group. Lusztig and Vogan have conjectured the existence of a natural bijection between the set of dominant integral weights of $G$, and the set of pairs consisting of a nilpotent orbit and a finite-dimensional irreducible representation of the isotropy group of the orbit. This conjecture has been proved by Bezrukavnikov. In this paper, we develop combinatorial algorithms for computing the bijection and its inverse in the case of $G = GL(n,\mathbb {C})$.
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Additional Information
  • Pramod N. Achar
  • Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
  • MR Author ID: 701892
  • Email: pramod@math.uchicago.edu
  • Received by editor(s): June 2, 2003
  • Received by editor(s) in revised form: January 19, 2004
  • Published electronically: May 24, 2004
  • Additional Notes: The author was partially supported by an NSF Graduate Research Fellowship, and later by an NSF Postdoctoral Research Fellowship.
  • © Copyright 2004 American Mathematical Society
  • Journal: Represent. Theory 8 (2004), 180-211
  • MSC (2000): Primary 22E46; Secondary 19A49
  • DOI: https://doi.org/10.1090/S1088-4165-04-00243-2
  • MathSciNet review: 2058726