| 구분 |
집중강연 |
| 일정 |
2017-12-26(화) 14:00~17:30 |
| 세미나실 |
129동 301호 |
| 강연자 |
Satoshi Naito (Tokyo Institute of Technology) |
| 담당교수 |
권재훈 |
| 기타 |
|
I will give a survey of the theory of (ordinary) Lakshmibai-Seshadri path model, due to P. Littelmann, for highest weight modules over Kac-Moody algebras;
an excellent reference is: Chapitre 8 of Prof. Kashiwara`s book "Bases cristallines des groupes quantiques, SMF, 2002".
The plan of my lecture is as follows:
(0) Standard notation for Kac-Moody algebras
(1) Definition of Lakshmibai-Seshadri (LS) paths and some of their basic properties
(2) Definition of root operators on LS paths and some of their basic properties
(3) Combinatorial character formula of Weyl-Kac type (in terms of LS paths) for highest weight modules
(4) Tensor products and concatenations of LS paths
(5) Kashiwara`s isomorphism theorem between crystal bases of highest weight modules and (ordinary) LS paths