Kazhdan-Lusztig Equivalence at the Iwahori Level

Abstract: We construct an equivalence between Iwahori-integrable representations of affine Lie algebras and representations of the "mixed" quantum group, thus confirming a conjecture by Gaitsgory. Our proof utilizes factorization methods: we show that both sides are equivalent to algebraic/topological factorization modules over a certain factorization algebra, which can then be compared via Riemann-Hilbert. On the quantum group side this is achieved via general machinery of homotopical algebra, whereas the affine side requires inputs from the theory of (renormalized) ind-coherent sheaves as well as compatibility with global Langlands over P1.

This is joint work with Lin Chen.

representation theory

Audience: researchers in the topic

MIT Lie groups seminar

Series comments: Description: Research seminar on Lie groups

This seminar will take place entirely online: Zoom Meeting Link. You should be able to watch live video at this link. Your microphone will be muted, but you are welcome to unmute it (microphone icon on the lower left of the Zoom window, perhaps visible only when you put your mouse near there) to ask a question.