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Summary: ON THE EQUIVARIANT K-THEORY OF THE NILPOTENT
CONE IN THE GENERAL LINEAR GROUP
PRAMOD N. ACHAR
Abstract. 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 finite-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 different contexts. In this paper, we
show that these two bijections for GL(n, C) coincide.
1. Introduction
Let G be a connected complex reductive Lie group, g its Lie algebra, and T a
maximal torus. Let +
be the set of dominant weights of G with respect to some
chosen Borel subgroup B containing T. Finally, let N be the nilpotent cone in g,
and let be the set of pairs
(C, E)
C N a nilpotent orbit,
and E an irreducible G-equivariant vector bundle on C
.
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