Resumen de Any flat bundle on a punctured disc has an oper structure

Edward Frenkel, Xinwen Zhu

• We prove that any flat $G$-bundle, where $G$ is a complex connected reductive algebraic group, on the punctured disc admits the structure of an oper. This result is important in the local geometric Langlands correspondence proposed in \cite{FG}. Our proof uses certain deformations of the affine Springer fibers which could be of independent interest. As a byproduct, we construct representations of affine Weyl groups on the homology of these deformations generalizing representations constructed by Lusztig.