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Representation Theory
Representation Theory
ISSN 1088-4165

 

On the equivariant $K$-theory of the nilpotent cone


Author: Viktor Ostrik
Journal: Represent. Theory 4 (2000), 296-305
MSC (2000): Primary 20G05; Secondary 14L30
Published electronically: July 31, 2000
MathSciNet review: 1773863
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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
Email: ostrik@mccme.ru

DOI: http://dx.doi.org/10.1090/S1088-4165-00-00089-3
PII: S 1088-4165(00)00089-3
Received by editor(s): November 16, 1999
Received by editor(s) in revised form: April 19, 2000
Published electronically: July 31, 2000
Article copyright: © Copyright 2000 American Mathematical Society