﻿ On the statistics of irreducible subrepresentations in large tensor powers of finite dimensional modules over simple Lie algebras (II)-清华大学求真书院

### On the statistics of irreducible subrepresentations in large tensor powers of finite dimensional modules over simple Lie algebras (II)

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

Nicolai Reshetikhin教授出生于前苏联列宁格勒，即现俄罗斯圣彼得堡。1982年，毕业于列宁格勒国立大学，获得学士学位与硕士学位。1984年，毕业于斯捷克洛夫数学研究所，获得博士学位。曾在哈佛大学、加州大学伯克利分校等知名大学任教。两次受邀在ICM国际数学家大会做报告，其中一次为大会报告。Reshetikhin教授的主要研究方向为量子拓扑，量子群及其表示，经典与量子可积系统，可积统计力学模型。他是量子群理论创始人之一、RT不变量的创始人之一、量子可积系统理论的重要推动人，泊松几何、辛几何的重要贡献者，Quantum Kac-Moody代数的重要贡献者、和量子引力有关的量子6j记号的奠基者。2021年，当选为美国数学会会士。

• ### Statistics of irreducible subrepresentations in large tensor powers of finite dimensional modules over simple Lie algebras

AbstractI 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...

• ### Infinite-dimensional Lie algebras and affine quantum groups

PrerequisiteYou should be familiar with fundamental notions in algebra and representation theory (basic ring theory, associative algebras, Lie algebras and their universal enveloping algebras, highest weight theory of finite-dimensional Lie algebras). This will be a useful background for the whole course. For the second part of the course, it will be good if you have followed a course on Hopf a...