Part 1. Quantum groups - 권재훈(서울대학교)
In this lecture, we give an introduction to the representation theory of quantum groups. After a brief review of the representation theory of semisimple Lie algebras (or symmetrizable Kac-Moody algebras), we introduce basic material about the representation theory of the quantum group, which would be necessary background for the next two parts of this lecture series. The topics will cover the integrable representations, classical limit, Lusztig braid symmetry, and PBW basis, and so on.
Part 2. Various bases for quantum groups - 박의용(서울시립대학교)
In this lecture, we explain the notions of crystal bases and global bases (canonical bases) for a quantum group and its highest weight modules. We then review the dual version of those bases and explain a connection with a PBW basis. In the case of type $A_n$, we explain combinatorial realizations of highest weight crystals including the tableaux realization.
Part 3. Application to cluster algebras - 김명호(경희대학교)
이 강연에서는 quantum unipotent coordinate ring $A_q(n)$의 quantum cluster algebra 구조를 설명하겠습니다. 다음과 같은 주제들을 다룰 예정입니다.
-Quantum unipotent coordinate ring $A_q(n)$의 정의
-Unipotent quantum minors
-(Quantum) cluster algebra의 정의
-Cluster algebra structure on $A_q(n)$ by C. Geiss, B. Leclerc and J. Schroer.