Any flat bundle on a punctured disc has an oper structure

• Autores: Edward Frenkel, Xinwen Zhu
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 17, Nº 1, 2010, págs. 27-38
• Idioma: inglés
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• Resumen

  • 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.