On the Equivariant K-Theory of the Nilpotent Cone in the General Linear Group

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 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