Any flat bundle on a punctured disc has an oper structure. (English) Zbl 1220.14013

Frenkel, Edward; Zhu, Xinwen

Math. Res. Lett. 17, No. 1, 27-37 (2010).

Let \(G\) be a complex connected reductive algebraic group. In this paper the authors use deformed versions of affine Springer fibers to show that any flat \(G\)-bundle on the punctured disc has an oper structure. Along the way the authors construct representations of affine Weyl groups on the homology of these deformed versions of affine Springer fibers.

Reviewer: Volodymyr Mazorchuk (Uppsala)

MSC:

14D24	Geometric Langlands program (algebro-geometric aspects)
17B67	Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
22E67	Loop groups and related constructions, group-theoretic treatment

Keywords:

reductive algebraic group; bundle; punctured disc; oper; Langlands correspondence; Springer fiber