Alexander Molev
(Sydney, Australia)
Feigin-Frenkel center for classical types.
Abstract: For each simple Lie algebra g consider the vacuum module V(g) at the critical level over the corresponding affine Kac-Moody algebra. The vacuum module has a vertex algebra structure. We construct explicit generators of the center of this vertex algebra for each Lie algebra g of classical type. This leads to a new proof of the Feigin-Frenkel theorem (1992) and to explicit constructions of commutative subalgebras of the universal enveloping algebras U(g[t]) and U(g). Moreover, we use Yangian characters (or q-characters) of Kirillov-Reshetikhin modules to calculate the images of the central elements under an affine version of the Harish-Chandra isomorphism.