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Let G be a simple complex algebraic group. Lusztig and Vogan have conjectured the existence of a natural bijection between the set of domi- nant integral weights of G, and the set of pairs consisting of a nilpotent orbit and a nite-dimensional irreducible representation of the isotropy group of the orbit. This conjecture was established by the author for G = GL(n;C), and by Bezrukavnikov for any G, in slightly dierent contexts. In this paper, we show that these two bijections for GL(n;C) coincide.

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