Representation theory of symmetric groups
Representation theory of symmetric groups is a classical topic with reach history and many intersections with other areas of mathematics and physics. The conventional approach to the theory, which goes back to Frobenius, Schur, and Young, is bases on ad hoc constructions, starting from the Young diagrams. We plan to present Vershik-Okounkov approach, where the corresponding objects appear naturally. The construction is based on the existence of the Gelfand-Tsetlin basis for the chain of symmetric groups, and Young diagrams appear as a convenient way to describe the spectrum of the Gelfand-Tsetlin algebra.
The second part of the course will be devoted to the asymptotic representation theory. We will focus on the Plancherel measure, one of the best known and well studied objects in the field, and discuss the famous Vershik-Kerov-Logan-Shepp limit shape theorem, as well as fluctuations (the celebrated Baik-Deift-Johansson Theorem).
The second part of the course will be devoted to the asymptotic representation theory. We will focus on the Plancherel measure, one of the best known and well studied objects in the field, and discuss the famous Vershik-Kerov-Logan-Shepp limit shape theorem, as well as fluctuations (the celebrated Baik-Deift-Johansson Theorem).
讲师
日期
2023年02月22日 至 05月24日
位置
Weekday | Time | Venue | Online | ID | Password |
---|---|---|---|---|---|
周三 | 15:20 - 16:55 | A3-3-103 | ZOOM 04 | 482 240 1589 | BIMSA |
周五 | 13:30 - 15:05 | A3-3-103 | ZOOM 04 | 482 240 1589 | BIMSA |
修课要求
Undergaduate Algebra, Probability and Functional Analysis
听众
Graduate
视频公开
公开
笔记公开
公开
语言
英文