Lakshmibai-Seshadri path model for highest weight modules over Kac-Moody algebras

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Lakshmibai-Seshadri path model for highest weight modules over Kac-Moody algebras

수리과학부 0 979
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

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