Summer School 2021: Enumerative Geometry, Physics and Representation Theory

Collection Summer School 2021: Enumerative Geometry, Physics and Representation Theory

Organizer(s) Organising Committee: Andrei Negut, Francesco Sala and Olivier Schiffmann; Scientific Committee: Mina Aganagic, Hiraku Nakajima, Nikita Nekrasov, and Andrei Okounkov
Date(s) 7/5/21 - 7/16/21
linked URL https://indico.math.cnrs.fr/event/5382/
00:00:00 / 00:00:00
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Gaiotto Conjectures for Quantum Super-groups

By Alexander Braverman

I am going to explain a series of conjectures due to D.Gaiotto which provide a geometric realization of categories of representations of certain quantum super-groups (such as U_q(gl(M|N)) via the affine Grassmannian of certain (purely even) algebraic groups. These conjectures generalize both the well-known geometric Satake equivalence and the so called Fundamental Local Equivalence of Gaitsgory and Lurie (which will be recalled in the talk).

In the 2nd part of the talk I will explain a recent proof of this conjecture for U_q(N|N-1) (for generic q), based on a joint work with Finkelberg and Travkin.

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