[Seminar 2021.04.02] Quantum affine analog of Kazhdan-Lusztig positivity for non-simply laced types via simply laced types

by qsms posted Mar 30, 2021
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일정시작 2021-04-02
배경색상 #7164D1

일시:  4월 2일 (금) 10:30 ~ 12:00

장소:  Zoom (ID: *)

제목:  Quantum affine analog of Kazhdan-Lusztig positivity for non-simply laced types via simply laced types.

연사:  오세진 교수 (이화여대)

 

초록:

In this talk, I will introduce the quantum affine analog of Kazhdan-Lusztig(KL) positivity conjecture suggested by Hernandez. The conjecture is already proved by Nakajima in a geometric way , when the quantum affine algebra is of simply-laced type. By establishing isomorphism between their Grothendieck rings for (simply-laced g_1 and non- simply-laced g_2) in a systematic way, we can propagate the positivity in simply laced type to non- simply laced type. Joining the result of Kashiwara-Kim-myself, we prove further that the (q,t)-character of each simple module of type $B$ is "canonical" $t$-deformtation of its q-character. This is joint work with Fujita-Hernandez-Oya (arXiv:2101.07489) and Fujita (arXiv:2007.03159).