| Speaker: | Yuchen Fu (Kyoto University) |
|---|---|
| Title: | Kazhdan-Lusztig Equivalence at the Iwahori Level |
| Date (JST): | Tue, Oct 18, 2022, 13:30 - 15:00 |
| Place: | Hybrid |
| Related File: | 2874.pdf |
| Abstract: | We construct an equivalence between Iwahori-integrable representations of affine Lie algebras and representations of the mixed quantum group, 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. |
