A Feigin-Frenkel theorem with n singularities

par Luca Casarin

lundi 16 janv. 2023, 10:30 → 12:30 Europe/Paris

Salle Fokko Ducloux (ICJ)

It is now a well know theorem by Feigin-Frenkel that the center of the completed enveloping algebra of the affine algebra ${\hat{\mathfrak{g}}}_k$ at the critical level is canonically isomorphic to the algebra of functions on the space of Opers
over the pointed formal disc $O{p}_{G^L}(D^{\ast })$. Starting from the work of Fortuna, Lombardo, Maffei and Melani I will introduce an analogue of the affine
algebra with n singularities. We then proceed to discuss an analogue of the
Feigin-Frenkel theorem in this new setting, which establishes an isomorphism
with the center of the completed enveloping algebra in the case with n
singularities with the algebra of functions on the space of Opers over the
n-pointed formal disc $O{p}_{G^L}(D_n^{\ast })$. I will focus on the main ingredients of the
proof and the various compatibilities that these isomorphisms satisfy with
respect to the original Feigin-Frenkel isomorphism.