2024 Combinatorics Workshop

Lusztig q weight multiplicities via affine crystals

30 Aug 2024, 09:30

1h

107 (Bldg. S1-6 (자연대6호관))

Invited talk Invited Talk

Speaker

Donghyun Kim

Description

Lusztig $q$ weight multiplicity is a polynomial in $q$ whose positivity has been verified by linking it to a specific affine Kazhdan-Lusztig polynomial. However, a combinatorial formula beyond type A has not been known until recently.

In 2019, Lee proposed a combinatorial formula for type C using a novel combinatorial concept known as semistandard oscillating tableaux. We will outline the proof of Lee's conjecture and discuss how it can be extended to type B spin weights case.

Based on joint work with Hyeonjae Choi and Seung Jin Lee.