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### 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...

• ### [YMSC-BIMSA Quantum Information Seminar] 27 A characterization of a finite-dimensional commuting square producing a subfactor of finite depth

摘要： We give a characterization of a finite-dimensional commuting square of C*-algebras that produces a hyperfinite type II_1 subfactor of finite index and finite depth in terms of Morita equivalent unitary fusion categories. This type of commuting squares were studied by N. Sato, and we show that a slight generalization of his construction covers the fully general case of such commuting squ...