Geometry Seminar

This talk is based on a joint work in progress with Gurbir Dhillon. A remarkable theorem of Feigin and E. Frenkel from the early 90's describes the center of the universal enveloping algebra of an (untwisted) affine Kac-Moody Lie algebra at the so called critical level proving a conjecture of Drinfeld: the center in question is the algebra of polynomial functions on an infinite dimensional affine space known as the space of opers. In our work we study a part of the center in positive characteristic p at an arbitrary non-critical level. Namely, we prove that the loop groupinvariants in the completed universal enveloping algebra is still the algebra of polynomials on an infinite dimensional affine space that is "p times smaller than the Feigin-Frenkel center''. In my talk I plan to introduce all necessary notions, state the result, explain motivations and examples.