北京雁栖湖应用数学研究院 北京雁栖湖应用数学研究院

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关于我们
院长致辞
理事会
协作机构
参观来访
人员
管理层
科研人员
博士后
来访学者
行政团队
学术研究
研究团队
公开课
讨论班
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教研人员
博士后
学生
会议
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论坛
学院生活
住宿
交通
配套设施
周边旅游
新闻
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资料下载
清华大学 "求真书院"
清华大学丘成桐数学科学中心
清华三亚国际数学论坛
上海数学与交叉学科研究院
BIMSA > Dualities and invariants with applications to asymptotic representation theory
Dualities and invariants with applications to asymptotic representation theory
In this course we will review classical invariant theory, discuss Howe duality for classical Lie groups and its extension to Lie superalgebras.
We will use the dualities for classical pairs of Lie groups to pose asymptotic questions. We will study representations of these dual pairs in the limit when ranks of the groups grow to infinity. We will then try to extend these results to Lie superalgebras. The material in this course is meant to provide deeper understanding and some missing proofs for results in my course "From free fermions to limit shapes and beyond", as well as pose new questions in asymptotic representation theory. Some connection will be made to the lectures of Pavel Nikitin "Representation theory of symmetric groups" and "Asymptotic representation theory".
Professor Lars Aake Andersson
讲师
Anton Nazarov
日期
2024年06月12日 至 09月06日
位置
Weekday Time Venue Online ID Password
周三,周五 15:20 - 16:55 A3-3-201 ZOOM 02 518 868 7656 BIMSA
修课要求
Representation theory of symmetric group, Lie groups and Lie algebras
课程大纲
1. Reminder on classical Lie algebras
2. Lie superalgebras
3. Irreducible finite-dimensional representations of simple Lie algebras
4. Schur-Weyl duality
5. Representations of Lie superalgebras
6. Classical invariant theory, first fundamental theorem for general linear group
7. First fundamental theorem for classical Lie groups
8. Howe duality for Lie superalgebras
9. Howe duality for infinite-dimensional Lie algebras
10. Insertion algorithms and algorithmic proofs of classical dualities
11. Howe duality in asymptotic representation theory, unitary representations of infinite-dimensional classical Lie groups
12. Young diagrams, tilings, lattice paths and other combinatorial realizations
13. Limit shapes
14. Asymptotic representation theory for Lie superalgebras
参考资料
[1] Goodman, Wallach "Symmetry, representations and invariants"
[2] Cheng, Wang "Dualities and representations of Lie superalgebras"
[3] Howe "Remarks on classical invariant theory"
[4] Howe "Perspectives on invariant theory: Schur duality, multiplicity-free actions and beyond"
[5] Olshanski "Unitary representations of infinite-dimensional pairs (G,K) and formalism of R. Howe"
听众
Graduate
视频公开
公开
笔记公开
公开
语言
英文
讲师介绍
Anton Nazarov is an associate professor at Saint Petersburg State University, Russia. He completed his PhD at the department of high-energy and elementary particle physics of Saint Petersburg State University in 2012 under the supervision of Vladimir Lyakhovsky. In 2013-2014 he was a postdoc at the University of Chicago. Anton's research interests are representation theory of Lie algebras, conformal field theory, integrable systems, determinantal point processes.
北京雁栖湖应用数学研究院
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No. 544, Hefangkou Village Huaibei Town, Huairou District Beijing 101408

北京市怀柔区 河防口村544号
北京雁栖湖应用数学研究院 101408

Tel. 010-60661855
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