Kazhdan-Lusztig Equivalence and Kac-Moody Localization


Fu, Y. (2023). Kazhdan-Lusztig Equivalence and Kac-Moody Localization. Perimeter Institute. https://pirsa.org/23110044


Fu, Yuchen. Kazhdan-Lusztig Equivalence and Kac-Moody Localization. Perimeter Institute, Nov. 02, 2023, https://pirsa.org/23110044


          @misc{ pirsa_PIRSA:23110044,
            doi = {10.48660/23110044},
            url = {https://pirsa.org/23110044},
            author = {Fu, Yuchen},
            keywords = {Mathematical physics},
            language = {en},
            title = {Kazhdan-Lusztig Equivalence and Kac-Moody Localization},
            publisher = {Perimeter Institute},
            year = {2023},
            month = {nov},
            note = {PIRSA:23110044 see, \url{https://pirsa.org}}


We will begin by reviewing the work of Kazhdan and Lusztig, who established an equivalence between certain affine Lie algebra representations and quantum group representations. It can be thought of as a logarithmic version of the CS-WZW correspondence. In a joint work with Lin Chen, we used factorization algebras to establish an extended version of this equivalence. We will explain the main structure of the proof, and draw some connections with Kazhdan and Lusztig's original proof. The key idea is that of Kac-Moody localization, a parametrized version of factorization homology. Time permitting, we will also explain how this idea plays a role in the recently announced proof (by Gaitsgory et al.) of the de Rham geometric Langlands conjecture.


Zoom link https://pitp.zoom.us/j/98932564942?pwd=WWdMLzI5WktkZnMrQmplU0J3Mk43dz09