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Elliptic Springer theory

Part of: Curves Lie groups

Published online by Cambridge University Press:  08 April 2015

David Ben-Zvi  and
David Nadler
David Ben-Zvi
Affiliation:
Department of Mathematics, University of Texas, Austin, TX 78712-0257, USA email benzvi@math.utexas.edu
David Nadler
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720-3840, USA email nadler@math.berkeley.edu
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Abstract

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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.

Keywords

Springer theoryprincipal bundles on elliptic curves

MSC classification

Primary: 22E57: Geometric Langlands program
Secondary: 14H60: Vector bundles on curves and their moduli
Type
Research Article
Information
Compositio Mathematica , Volume 151 , Issue 8 , August 2015 , pp. 1568 - 1584
Copyright
© The Authors 2015 

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