Fundamental local equivalences in quantum geometric Langlands

          @misc{ pirsa_PIRSA:20060038,
            doi = {10.48660/20060038},
            url = {https://pirsa.org/20060038},
            author = {Dhillon, Gurbir},
            keywords = {Mathematical physics},
            language = {en},
            title = {Fundamental local equivalences in quantum geometric Langlands},
            publisher = {Perimeter Institute},
            year = {2020},
            month = {jun},
            note = {PIRSA:20060038 see, \url{https://pirsa.org}}
          }
          

Abstract

In quantum geometric Langlands, the Satake equivalence plays a less prominent role than in the classical theory. Gaitsgory--Lurie proposed a conjectural substitute, later termed the fundamental local equivalence, relating categories of arc-integrable Kac--Moody representations and Whittaker D-modules on the affine Grassmannian. With a few exceptions, we verified this conjecture non-factorizably, as well as its extension to the affine flag variety. This is a report on joint work with Justin Campbell and Sam Raskin.