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.
Lecturer
Date
21st February ~ 16th May, 2023
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Tuesday,Thursday | 13:30 - 15:05 | A3-1-101 | ZOOM 05 | 293 812 9202 | BIMSA |
Prerequisite
Lie algebras, representations.
Syllabus
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.
Audience
Graduate
Video Public
Yes
Notes Public
Yes
Language
English
Lecturer Intro
Ievgen Makedonskyi obtained a PhD degree in mathematics from the Russian University of Advanced Economic Research and then worked at the Russian University of Advanced Economic Research, the Max Planck Institute of Mathematics, the University of Tokyo, Skolkovo University of Science and Technology, and Jena University in Germany. In 2022, he joined the Yanqi Lake Beijing Institute of Mathematical Sciences and Applications as an assistant professor. His research interests include Lie algebra, polynomial derivation, affine Kac Moody Lie algebra, Weyl and Demazure module Asymmetric Macdonald polynomials, recent algebras, arc varieties, etc.