Weyl modules and opers without monodromy

Abstract

We prove that the algebra of endomorphisms of a Weyl module of critical level is isomorphic to the algebra of functions on the space of monodromy-free opers on the disc with regular singularity and residue determined by the highest weight of the Weyl module. This result may be used to test the local geometric Langlands correspondence proposed in our earlier work arXiv:math/0508382.

18 pages

References in corpus (1)

• Affine Algebras, Langlands Duality and Bethe Ansatz

Cited by in corpus (5)

• Local Geometric Langlands Correspondence: the Spherical Case
• Characters of representations of affine Kac-Moody Lie algebras at the critical level
• Algebras of twisted chiral differential operators and affine localization of $\mathfrak{g}$-modules
• On the endomorphisms of Weyl modules over affine Kac-Moody algebras at the critical level
• A chiral Borel-Weil-Bott theorem