Representations of classical Lie algebras and combinatorics of their branching rules
|분야||2017 Math Colloquium|
|날짜||2017-05-26||시간||15:50 ~ 18:00|
|장소||Math Sci Bldg 404||초청자||YoungJu Choie, Jae Choon Cha|
|연사||Jae-Hoon Kwon||소속||Seoul National Univ.|
|TOPIC||Representations of classical Lie algebras and combinatorics of their branching rules|
|소개 및 안내사항||Title: Representations of classical Lie algebras and combinatorics of their branching rules
Abstract: The theory of crystal basis provides a powerful tool to study combinatorial structure of representations of Kac-Moody algebras and their quantum groups. In this talk, we introduce a new combinatorial model for irreducible characters of simple Lie algebras of classical type BCD, which is obtained by applying the crystal basis theory to the higher level fermionic Fock space. As one of its applications, we explain how classical branching rules of irreducible characters in a stable range, including the well-known Littlewood restriction rule, can be extended to arbitrary highest weights in a bijective way.