Fundamental local equivalences in quantum geometric Langlands

Abstract

In quantum geometric Langlands, the Satake equivalence plays a less prominent role than in the classical theory. Gaitsgory--Lurie proposed a conjectural substitute, later termed the fundamental local equivalence. With a few exceptions, we prove this conjecture and its extension to the affine flag variety by using what amount to Soergel module techniques.

31 pages, comments welcome

References in corpus (4)

• Loop group actions on categories and Whittaker invariants
• Outline of the proof of the geometric Langlands conjecture for GL(2)
• Endoscopy for Hecke categories, character sheaves and representations
• Twisted geometric Langlands correspondence for a torus

Cited by in corpus (4)

• An Extension of the Kazhdan-Lusztig Equivalence
• Twisted Whittaker category on affine flags and the category of representations of the mixed quantum group
• The Drinfeld--Sokolov reduction of admissible representations of affine Lie algebras
• Affine Harish-Chandra bimodules and Steinberg--Whittaker localization