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

##### 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
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