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Deformations of nilpotent cones and Springer correspondences

From: American Journal of Mathematics
Volume 133, Number 2, April 2011
pp. 519-553 | 10.1353/ajm.2011.0014

Abstract

Abstract:

Let $G = \mathop{Sp}( 2n )$ be the symplectic group over ${\Bbb Z}$. We present a certain kind of deformation of the nilpotent cone of $G$ with $G$-action. This enables us to make direct links between the Springer correspondence of ${\frak{sp}} _{2n}$ over ${\Bbb C}$, that over characteristic two, and our exotic Springer correspondence. As a by-product, we obtain a complete description of our exotic Springer correspondence.