English

Any flat bundle on a punctured disc has an oper structure

Representation Theory 2010-01-28 v2 Algebraic Geometry Quantum Algebra

Abstract

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 arXiv:math/0508382. 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.

Keywords

Cite

@article{arxiv.0811.3186,
  title  = {Any flat bundle on a punctured disc has an oper structure},
  author = {Edward Frenkel and Xinwen Zhu},
  journal= {arXiv preprint arXiv:0811.3186},
  year   = {2010}
}

Comments

12 pages

R2 v1 2026-06-21T11:43:24.525Z