Seminar in Representation Theory

主講者: | Jae-Hoon Kwon (Seoul National University) |

講題: | Lusztig t-weight multiplicity at weight 0 |

時間: | 2020-01-16 (Thu.) 15:00 - 16:00 |

地點: | 數學所 722 研討室 (台大院區) |

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 Schutzenberger. 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). |

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