Representation theory of finite-dimensional Lie algebras and superalgebras part 2
We will study the classification of finite-dimensional representations of semi-simple Lie algebras via highest weight. Then we will discuss the representation theory of Lie algebras of some special types, in particular Schur-Weyl duality. Then we will go to Lie superalgebras and will discuss the structure of their representations. If we will have enough time we will discuss Sergeev duality and papers of Brundan-Stroppel.
Lecturer
Date
19th February ~ 22nd May, 2025
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Thursday,Wednesday | 15:20 - 16:55 | A3-2a-201 | ZOOM 07 | 559 700 6085 | BIMSA |
Prerequisite
Linear algebra, Coxeter groups, Root systems, lattices, classification of finite-dimensional Lie algebras.
Reference
Humphreys J. E. Introduction to Lie Algebras and Representation Theory
arXiv:0907.2543 Highest weight categories arising from Khovanov's diagram algebra IV: the general linear supergroup, Jonathan Brundan, Catharina Stroppel.
arXiv:0907.2543 Highest weight categories arising from Khovanov's diagram algebra IV: the general linear supergroup, Jonathan Brundan, Catharina Stroppel.
Audience
Undergraduate
, Advanced Undergraduate
, Graduate
, Postdoc
, Researcher
Video Public
Yes
Notes Public
No
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.