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We prove that any flat G-bundle, where G is a complex connected reductivealgebraic group, on the punctured disc admits the structure of an oper. Thisresult is important in the local geometric Langlands correspondence proposed inarXiv:math/0508382. Our proof uses certain deformations of the affine Springerfibers which could be of independent interest. As a byproduct, we constructrepresentations of affine Weyl groups on the homology of these deformationsgeneralizing representations constructed by Lusztig.

Any flat bundle on a punctured disc has an oper structure