创新团队讨论班

系列学术报告

报告人：姚裕丰（博士， 李代数及其表示）

题目： Modular representations of reductive Lie algebras and primitive ideals of enveloping algebras（II）

时间： 2010年 1月 5 日 （周二） 下午 14：30-16：20

地点： 4号教学楼402多媒体教室

摘要

In this series of lectures, we will discuss modular representations of reductive Lie algebras and related topics on primitive ideals of enveloping algebras. We will start with some fundamentals of the modular representation theory and compare it with the classical representation theory in characteristic 0, which was developed much earlier.

The Kac-Weisfeiler-Friedlander-Parshall Morita equivalence will be discussed, and then the well-known Kac-Weisfeiler conjecture (Premet's Theorem) will be introduced and Premet's proof of this conjecture will be sketched.

After that, we will briefly introduce recent work of Bezrukavnikov –Mirkovic -Rumynin on a more geometric description of modular representations of reductive Lie algebras. Finally, we will further discuss primitive ideals of enveloping algebras and relate modular representations with Azumaya loci and smooth loci of the center of the enveloping algebras.