学术报告

日本东京大学数学系齐藤义久 (Saito Yoshihisa) 教授将在2015年10月27日至11月5日在同济大学数学系致远楼107教室作关于《晶体基的几何结构及其应用》的系列讲座, 每次二小时左右, 热烈欢迎有兴趣的同行参加, 具体日程安排如下:

10月27，28，30日 (星期二，三，五) 下午14:00-16:30

11月2，3，4，6日(星期一，二，三，五) 下午14:00-16:30

题目: Geometric construction of crystal bases and its applications

摘要: This series of lectures is divided into three parts. In the first part, we will give precise definitions of crystal and canonical (=global crystal) bases of quantum universal enveloping algebras, and introduce their basic properties in algebraic point of view. In the second part, we will explain how to reformulate the above terminologies in geometrical language. In our geometric construction, certain varieties associated quivers, so-called “quiver varieties” are used. In geometric point of view, crystal bases are identified with the sets of irreducible Lagrangian subvarieties of quiver varieties, and canonical bases are identified with certain simple perverse sheaves on quiver varieties. In the third part, we restrict ourselves in type A. In this case, a quiver variety can be identified with a subvariety of a “flag variety”.

Under the identification above, some problems on flag varieties in type A can be translated to that of quiver varieties in type A. As an application of this identification, we will explain an approach to some problems in (geometric) representation theory of Weyl groups, by using our geometric construction.