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Elliptic Springer theory
Published online by Cambridge University Press: 08 April 2015
Abstract
We introduce an elliptic version of the Grothendieck–Springer sheaf and establish elliptic analogues of the basic results of Springer theory. From a geometric perspective, our constructions specialize geometric Eisenstein series to the resolution of degree-zero, semistable $G$-bundles by degree-zero
$B$-bundles over an elliptic curve
$E$. From a representation theory perspective, they produce a full embedding of representations of the elliptic or double affine Weyl group into perverse sheaves with nilpotent characteristic variety on the moduli of
$G$-bundles over
$E$. The resulting objects are principal series examples of elliptic character sheaves, objects expected to play the role of character sheaves for loop groups.
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- Research Article
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- © The Authors 2015
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