Speaker : Jae-Hoon Kwon (Seoul National University)
Title : Lusztig t-weight multiplicity at weight 0
Time : 2020-01-16 (Thu) 15:00 - 16:00
Place : Seminar Room 722, Institute of Mathematics (NTU Campus)
Abstract: The Lusztig t-weight multiplicity is a t-analogue of the weight multiplicities of finite-dimensional irreducible modules over semisimple Lie algebras. It is equal to an affine Kazhdan-Lusztig polynomial which has positivity. There is another combinatorial proof of the positivity of t-weight multiplicity for type A due to Lascoux and Sch├╝tzenberger. But no generalization of it for other types is known in general. Recently, Lecouvey and Lenart gave a combinatorial formula for the t-weight multiplicity at weight 0 for type C and hence proved its positivity, using the spinor model of crystals of classical type. In this talk, we give a formula for the t-weight multiplicity at weight 0 for type B and D. It is based on our new formula for the branching rule associated to the pair $(GL_n,O_n)$. This is a joint work with I.S. Jang (arXiv:1908.11041).