An Extension of the Kazhdan-Lusztig Equivalence
Open/View files
Date
May 3, 2022
Author(s)
Fu, Yuchen
The Harvard community has made this article openly available. Please share how this access benefits you.
Citation
Fu, Yuchen. 2022. An Extension of the Kazhdan-Lusztig Equivalence. Doctoral dissertation, Harvard University Graduate School of Arts and Sciences.
Abstract
We establish an equivalence between the DG category of Iwahori–integrable affine Lie algebra representations and the DG category of representations of the “mixed” quantum group, thus confirming a conjecture made by D. Gaitsgory. This result is a tamely ramified version of an equivalence established by D. Kazhdan and G. Lusztig in the spherically integrable setting. Our proof, which utilizes the notion of factorization algebras introduced by A. Beilinson and V. Drinfeld, is independent from the original Kazhdan–Lusztig equivalence. Along the way we establish several results in the quantum local geometric Langlands program.
The work reported here was done jointly with L. Chen.
Terms of Use
This article is made available under the terms and conditions applicable to Other Posted Material (LAA), as set forth at Terms of Service
Subjects
Collection