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

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- by Viktor Ostrik
- Represent. Theory
**4**(2000), 296-305 - DOI: https://doi.org/10.1090/S1088-4165-00-00089-3
- Published electronically: July 31, 2000
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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 $\mathcal O$}.## References

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## Bibliographic 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