Coxeter groups, Hecke algebras and Macdonald polynomials
we will define and study Coxeter groups and their action by reflections. The main examples of them are Weyl groups of Lie algebras. In the case of finite-dimensional Lie algebras they have a natural extensions called affine Weyl groups. We will focus on the affine analogues of affine Weyl groups. They are called double affine Weyl groups.
Group algebras of Coxeter groups have a natural deformation called Hecke algebras. We will study double affine Hecke algebras which correspond to double affine Weyl groups. These algebras have the most important representations called polynomial representations. These representations have a natural basis called Nonsymetric Macdonald polynomials. We will explain the various properties of these polynomials, relations to representation theory and integrable systems.
Group algebras of Coxeter groups have a natural deformation called Hecke algebras. We will study double affine Hecke algebras which correspond to double affine Weyl groups. These algebras have the most important representations called polynomial representations. These representations have a natural basis called Nonsymetric Macdonald polynomials. We will explain the various properties of these polynomials, relations to representation theory and integrable systems.
Lecturer
Date
19th September ~ 13th December, 2023
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Tuesday,Wednesday | 15:20 - 16:55 | A3-1a-205 | ZOOM 08 | 787 662 9899 | BIMSA |
Prerequisite
Basic course of algebra, linear algebra and basic group theory.
Audience
Undergraduate
, Graduate
Video Public
Yes
Notes Public
Yes
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.