BIMSA > BIMSA-Tsinghua Quantum Symmetry Seminar On the statistics of irreducible subrepresentations in large tensor powers of finite dimensional modules over simple Lie algebras
On the statistics of irreducible subrepresentations in large tensor powers of finite dimensional modules over simple Lie algebras
Organizers
Lin Zhe Huang , Zheng Wei Liu , Sébastien Palcoux , Yi Long Wang , Jin Song Wu
Speaker
Nicolai Reshetikhin
Time
Wednesday, December 7, 2022 10:30 AM - 12:00 PM
Venue
Online
Online
Zoom 537 192 5549 (BIMSA)
Abstract
I will explain the solution to the following problem. Given a finite dimensional irreducible representation of a simple Lie algebra, consider its N-th tensor power. It has a decomposition into the direct sum of irreducible modules. The problem is how to find the asymptotic of multiplicities of irreducible subrepresentations in the limit N \to \infty and how to find the asymptotic of the Plancherel and character measures on the set of irreducible components in this limit.
Speaker Intro
Professor Nicolai Reshetikhin was born in Leningrad, former Soviet Union, now St. Petersburg, Russia. In 1982, he graduated from Leningrad State University with a bachelor's degree and a master's degree. In 1984, he graduated from the Steklov Institute of Mathematics and obtained a PhD degree. He has taught at well-known universities such as Harvard University, the University of California, Berkeley and the University of Amsterdam. He was invited twice to give a talk at the ICM International Conference of Mathematicians, one of which was a plenary talk. Professor Reshetikhin's main research interests include quantum topology, quantum groups and their representations, classical and quantum integrable systems, and integrable models statistical mechanics. He is one of the founders of quantum group theory, one of the authors of Reshetikhin-Turaev invariant, has important results in the theory of quantum integrable system, in Poisson and symplectic geometry, in the theory of quantum Kac Moody algebra. In 2010, he was elected as a Foreign member of the Royal Danish Academy. In 2021, he became a Fellow of the American Mathematical Society.