Representations of current Lie algebras
I will start from the reminder of the representation theory of simple finite-dimensional Lie algebras. Then I will define the current algebras and some the most important representations of them. I will explain how are these modules related to some families of orthogonal polynomials, describe the structure of these modules.
讲师
日期
2023年02月21日 至 05月16日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周二,周四 | 13:30 - 15:05 | A3-1-101 | ZOOM 05 | 293 812 9202 | BIMSA |
修课要求
Lie algebras, representations.
课程大纲
Recall the representation theory of finite-dimensional Lie algebras. Define the current algebras. Explain the smallest example. Define Local and Weyl modules. Define fusion product and prove the lower bound for the dimension of the Weyl module. Chari-Loktevs proof of the upper bound for type A. Define nonsymmetric Macdonald polynomials and the formulas for them. Orr-Shimozono formula for specializations of nonsymmetric Macdonald polynomials. Generalized Weyl modules and decomposition procedure. Upper bound for the dimension in general. Computation of the characters. Freeness of the global Weyl module over highest weight algebra.
听众
Graduate
视频公开
公开
笔记公开
公开
语言
英文
讲师介绍
Ievgen Makedonskyi于俄罗斯高等经济研究大学获得数学博士学位，先后在俄罗斯高等经济研究大学、马克斯普朗克数学研究所、东京大学、斯科尔科沃科技大学、德国耶拿大学任职，2022年加入北京雁栖湖应用数学研究院任助理研究员，研究兴趣包括李代数、多项式导子、仿射Kac-Moody李代数、Weyl和Demazure模、非对称Macdonald多项式、近世代数、弧簇等。