Algebra Seminar
Ivan Loseu, Yale
Harish-Chandra centers for affine Kac-Moody algebras in positive characteristic Abstract : This talk is based on a joint work in progress with Gurbir Dhillon. A remarkable theorem of Feigin and E. Frenkel from the early 90s 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 algebra of 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 motivations and examples.
4:00PM, Zoom (please email achirvas@buffalo.edu)
Title: Harish-Chandra centers for affine Kac-Moody algebras in positive characteristic
Abstract : This talk is based on a joint work in progress with Gurbir Dhillon. A remarkable theorem of Feigin and E. Frenkel from the early 90s 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 algebra of 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 motivations and examples.