学术报告报告主题: Yangians, super-Yangians and their representations
报告人: Alexander Molev
报告时间：2023年10月26日（星期四）上午10:00-11:00
2023年10月26日（星期四）上午11:00-12:00
2023年10月27日（星期五）下午14:00-15:00
2023年10月27日（星期五）下午15:00-16:00
2023年10月30日（星期一）上午10:00-11:00
2023年10月30日（星期一）上午11:00-12:00
2023年11月02日（星期四）上午10:00-11:00
2023年11月02日（星期四）上午11:00-12:00
2023年11月03日（星期五）下午14:00-15:00
2023年11月03日（星期五）下午15:00-16:00
报告地点：37号楼3A02
邀请人: 刘明 副教授
欢迎广大师生前往！
数学学院
2023年10月23日
报告摘要：
By the original definition of Drinfeld (1985), the Yangian Y(a) associated with a simple Lie algebra a is a canonical deformation of the universal enveloping algebra U(a[u]) in the class of Hopf algebras. The representation theory of the Yangians is a substantive and fascinating area which has since attracted significant interest from both mathematical physicists and representation theorists.
The Yangians associated with different families of Lie superalgebras were subsequently introduced by Nazarov (1991, 1992) and Arnaudon et al. (2003). A revival of interest to representation theory of the super-Yangians from several groups of researchers has been observed in resent years, although many basic problems still remain open.
The goal of the course is to give an introduction to the theory of Yangians, their super-counterparts and discuss known results and open problems in the representation theory. We will begin with a review of the Yangians associated with the general linear Lie algebras and superalgebras, whose structure and representations are best understood. We will obtain a description of finite-dimensional irreducible representations of these algebras and see how such generic representations can be constructed. Then we will move to the orthogonal, symplectic and orthosymplectic Yangians and review analogous descriptions of the representations in those cases where they are known. We will discuss the obstacles on the way in the super-cases which include most of the Yangians associated with the orthosymplectic and ‘strange’ Lie superalgebras.
报告人介绍：
Molev 是悉尼大学教授，澳大利亚科学院院士，国际著名表示论专家，在Yangian 代数、组合数学等诸多研究领域都作出了重要的贡献。Molev 教授2001年获得澳大利亚数学会奖。在Inventiones mathematicae，Duke mathematical journal，Advances in Mathematics 等国际知名期刊发表文章90多篇。