中国科学院数学与系统科学研究院

数学研究所

数学科学全国重点实验室

学术报告

表示论讨论班

Speaker: Losev教授（Yale University）

Inviter: 聂思安

Language: English

Title: Harish-Chandra center for affine Kac-Moody algebras in positive characteristic 

Time & Venue: 2026年1月9日（星期五） 14:40 - 15:40 &Zoom会议: 875 7095 0404密码：336195

Abstract: This talk is based on a joint work in preparation 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 plan to introduce all necessary notions, state the result, explain motivations and examples.