MIT Lie Groups Seminar
Wednesday, February 23, 2022 at 4:00pm to 5:00pm
Building 2, 2-142
182 MEMORIAL DR, Cambridge, MA 02139
Speaker: Yuchen Fu (Harvard University)
Title: 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.
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