Elliptic Springer Theory

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.

13 pages. Comments welcome!

References in corpus (1)

• Noncommutative Counterparts of the Springer Resolution

Cited by in corpus (8)

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• Uniformization of semistable bundles on elliptic curves
• KLR and Schur algebras for curves and semi-cuspidal representations
• The Jordan--Chevalley decomposition for $G$-bundles on elliptic curves
• On the stack of semistable $G$-bundles over an elliptic curve