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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
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by Viktor Ostrik PDF
Represent. Theory 4 (2000), 296-305 Request permission

Abstract:

In this note we construct a “Kazhdan-Lusztig type” basis in equivariant $K$-theory of the nilpotent cone of a simple algebraic group $G$. This basis conjecturally is very close to the basis of this $K$-group consisting of irreducible bundles on nilpotent orbits. As a consequence we get a natural (conjectural) construction of Lusztig’s bijection between dominant weights and pairs {nilpotent orbit $\mathcal O$, irreducible $G$-bundle on $\mathcal O$}.
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Additional Information
  • Viktor Ostrik
  • Affiliation: Independent Moscow University, 11 Bolshoj Vlasjevskij per., Moscow 121002 Russia
  • MR Author ID: 601011
  • Email: ostrik@mccme.ru
  • Received by editor(s): November 16, 1999
  • Received by editor(s) in revised form: April 19, 2000
  • Published electronically: July 31, 2000
  • © Copyright 2000 American Mathematical Society
  • Journal: Represent. Theory 4 (2000), 296-305
  • MSC (2000): Primary 20G05; Secondary 14L30
  • DOI: https://doi.org/10.1090/S1088-4165-00-00089-3
  • MathSciNet review: 1773863