报告人：张健 华中师范大学教授

报告时间：6月25日15:00

报告地点：学院南阶教室

主办单位：数学与统计学院

欢迎光临！

   报告摘要：A classical paper of Gelfand and Tsetlin describes a basis of irreducible finite dimensional modules over the Lie algebra gl_n. This is one of the most remarkable results of the representation theory of Lie algebras which initiated a development of the theory of Gelfand-Tsetlin modules. The Gelfand-Tsetlin modules form the largest subcategory of gl_n-modules where there is some understanding of irreducible modules. The main remaining problem is how to construct explicitly these modules. We propose a new effective method of constructing explicitly Gelfand -Tsetlin modules for gl_n and obtain a large family of irreducible modules that have a basis consisting of Gelfand-Tsetlin tableaux and the action of the Lie algebra is given by the  Gelfand-Tsetlin formulas. As an application of our construction we prove necessary and sufficient condition for the Gelfand and Graev's continuation construction  to define a module which was conjectured by Lemire and Patera. The talk is based on joint results with Vyacheslav Futorny and Luis Enrique Ramirez.

  张健，华中师范大学教授。2015年获华南理工大学博士学位，2016年至2020年先后在巴西圣保罗大学、中国台湾等地从事博士后工作。主要研究方向为李代数、量子群、表示论。在Advances in Mathematics, Mathematische Zeitschrift等期刊发表学术论文十余篇。