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Representation Theory

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On the equivariant K-theory of the nilpotent cone in the general linear group

Author: Pramod N. Achar
Journal: Represent. Theory 8 (2004), 180-211
MSC (2000): Primary 22E46; Secondary 19A49
Published electronically: May 24, 2004
Corrigendum: Represent. Theory 20 (2016), 414-418.
MathSciNet review: 2058726
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Abstract: Let $G$ be a simple complex algebraic group. Lusztig and Vogan have conjectured the existence of a natural bijection between the set of dominant integral weights of $G$, and the set of pairs consisting of a nilpotent orbit and a finite-dimensional irreducible representation of the isotropy group of the orbit. This conjecture has been proved by Bezrukavnikov. In this paper, we develop combinatorial algorithms for computing the bijection and its inverse in the case of $G = GL(n,\mathbb {C})$.

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Additional Information

Pramod N. Achar
Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
MR Author ID: 701892

Received by editor(s): June 2, 2003
Received by editor(s) in revised form: January 19, 2004
Published electronically: May 24, 2004
Additional Notes: The author was partially supported by an NSF Graduate Research Fellowship, and later by an NSF Postdoctoral Research Fellowship.
Article copyright: © Copyright 2004 American Mathematical Society