Affine Beilinson-Bernstein localization at the critical level for $G{L}_2$

Abstract

We prove the rank 1 case of a conjecture of Frenkel-Gaitsgory: critical level Kac-Moody representations with regular central characters localize onto the affine Grassmannian. The method uses an analogue in local geometric Langlands of the existence of Whittaker models for most representations of $G{L}_2$ over a non-Archimedean field.

References in corpus (6)

• Loop group actions on categories and Whittaker invariants
• Sheaves of categories and the notion of 1-affineness
• Quantum Langlands Correspondence
• Homological methods in semi-infinite contexts
• Irreducible connections admit generic oper structures
• A generalization of the b-function lemma

Cited by in corpus (6)

• Homological methods in semi-infinite contexts
• Equivariant localization in factorization homology and applications in mathematical physics I: Foundations
• Equivariant localization in factorization homology and applications in mathematical physics II: Gauge theory applications
• Localization for affine $W$-algebras
• An Extension of the Kazhdan-Lusztig Equivalence
• Categorical Moy-Prasad theory