Infinite-Dimensional Algebra Seminar: Ivan Loseu (Yale)

Building 2, Room 135

Speaker: Ivan Loseu (Yale University)Where: In-Person at MIT Room 2-135 and onZoom: https://mit.zoom.us/j/94469771032?pwd=d3JaSVhVV0xDOGpkUDdveXdOYmNXQT09Title: Harish-Chandra center for affine Kac-Moody algebras in positive characteristicAbstract: 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 group invariants 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 will introduce all necessary notions, state the result, explain examples, motivations and some ideas of the proof.