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Representation Theory

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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
MR Author ID: 601011

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