On the equivariant 𝐾-theory of the nilpotent cone

Ostrik, Viktor

doi:10.1090/S1088-4165-00-00089-3

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 $\mathcal O$}.

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