Representation Theory Seminar at KIAS, Korea
2013/09/24 (Tue)
speaker: Jae-Hoon Kwon (SungKyunKwan Univ.)
time and venue: 16:00 - 18:00, Room 1423, KIAS, Seoul, Korea
title : Super duality and irreducible characters of Lie superalgebras 1,2
abstract:
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Super duality is an equivalence between a parabolic BGG category of the classical Lie algebras and a category of the basic classical Lie superalgebras. It was recently established by Cheng and Lam for type A, and by Cheng, Lam and Wang for type BCD. One of its most remarkable features is that super duality reveals a natural connection with the Kazhdan-Lusztig theory of Lie algebras and therefore enables us to describe a large family of irreducible characters including finite dimensional irreducible characters in terms of classical Kazhdan-Lusztig polynomials, which was a longstanding problem since late 70's after the Kac's classification of finite dimensional complex simple Lie superalgebras. In the first talk, we give a brief introduction to super duality focusing on type A. In the second talk, we will introduce some applications. |