Speaker :
 JaeHoon Kwon (Seoul National University) 
Title :

Lusztig tweight multiplicity at weight 0 
Time :
 20200116 (Thu) 15:00  16:00 
Place : 
Seminar Room 722, Institute of Mathematics (NTU Campus) 
Abstract: 
The Lusztig tweight multiplicity is a tanalogue of the weight multiplicities of finitedimensional irreducible modules over semisimple Lie algebras. It is equal to an affine KazhdanLusztig polynomial which has positivity. There is another combinatorial proof of the positivity of tweight multiplicity for type A due to Lascoux and Schützenberger. But no generalization of it for other types is known in general. Recently, Lecouvey and Lenart gave a combinatorial formula for the tweight 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 tweight 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). 