Geometric Satake equivalence for some algebraic supergoups

Mardi 12 mai 14:00-15:15 - Alexander Braverman - Université de Toronto

Résumé : Lien vers la video
In the beginning of the talk I shall review the geometric
Satake equivalence (both usual and derived) and also the so called
« fundamental local equivalence » of Gaitsgory and Lurie (all the
statements interpret certain category of sheaves on the affine
Grassmannian of a reductive group G in terms of the Langlands dual
group). In the 2nd part of the talk we shall present a series of
conjectural generalizations of these statements (due to D. Gaiotto)
for the group GL(n).
Namely, we shall discuss some other categories of sheaves on the
affine Grassmannian of GL(n) and interpret them in terms of
representations of some (quantum) super-groups (the statements are
known for q=1 (the parameter of the quantum group) - the proof of
Gaiotto conjectures in this case is my joint work with Ginzburg,
Finkelberg and Travkin). If time permits, I shall discuss the relation
of these ideas to the work of Ben Zvi, Sakellaridis and Venkatesh
which provides a geometric intuition behind the well known relation
between (some) periods of automorphic forms and values of automorphic
L-functions.

Lieu : Séminaire en ligne

Geometric Satake equivalence for some algebraic supergoups  Version PDF