主讲人：林宗柱教授，

工作单位：Kansas state University and Henan University

Title: Representation theory of towers of algebras and  an introduction to Gelfand-Zetlin theory

Abstract : For a given towers of groups such as  symmetric groups $S_n\subseteq S_{n+1}$ as a subgroups, Vershik and Okounkov started a new representation theory using ideas from Gelfand-Zetlin to consider all these groups at once. In this way, almost all classical theory of constructing irreducible representations symmetric groups can be reconstructed. This idea has been applied to a wider range of representation theories such as representation theory of classical Lie algebra by Molev and many others. It is also applied to Heck algebras and other finite dimensional semisimple algebras. In this series of lectures, I will set up the representation theory for towers of not-necessarily semisimple algebras and will construct basis for projective modules, simple modules, injective modules in terms of the corresponding branching graphs, also called Gelfand-Zetlin graphs. Then I will apply this theory to a tower of algebras arising from Rota-Baxter algebras through repeated extension similar to Jone's construction of towers of algebra from subfactors of type II_1 to get temperley Lie algebras. I will give construction of the corresponding fock spaces with basis consisting certain diagrams similar to young diagrams.  Later I will also apply the theory to a tower of algebras from view point of Okada by using more general variables to get a sheaf of towers of algebras over an algebraic varieties. Hopefully these will provide a model of constructing wall-crossing structures.  These towers of algebra are closed related to rooted binary trees (the branch graph of irreducible modules) which is misteriously related the channel polarization construction by Arikan. This leads to a possible categorificaion of a channel polarization.

时间及地点：

Lecture 1: 5.27 15:00-17:30 数学与统计学院北研究生教室；

Lecture 2：5.28 15:00-17:30 数学与统计学院南研究生教室；

Lecture 3：5. 29 15:00-17:30 数学与统计学院北研究生教室。