PIRSA:20060038 Conference Mathematical physics

DOI10.48660/20060038

Conference/School: Geometric Representation Theory

Dhillon, G. (2020). Fundamental local equivalences in quantum geometric Langlands. Perimeter Institute. https://pirsa.org/20060038

Dhillon, Gurbir. Fundamental local equivalences in quantum geometric Langlands. Perimeter Institute, Jun. 22, 2020, https://pirsa.org/20060038 

@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.

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