1 results
Elliptic Springer theory
- Part of
-
- Journal:
- Compositio Mathematica / Volume 151 / Issue 8 / August 2015
- Published online by Cambridge University Press:
- 08 April 2015, pp. 1568-1584
- Print publication:
- August 2015
-
- Article
-
- You have access
- Export citation
-
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.
