Jantzen filtration of Weyl modules, product of Young symmetrizers and denominator of Young’s seminormal basis

Author:

Fang Ming,Lim Kay Jin,Tan Kai

Abstract

Let G G be a connected reductive algebraic group over an algebraically closed field of characteristic p > 0 p>0 , Δ ( λ ) \Delta (\lambda ) denote the Weyl module of G G of highest weight λ \lambda and ι λ , μ : Δ ( λ + μ ) Δ ( λ ) Δ ( μ ) \iota _{\lambda ,\mu }:\Delta (\lambda +\mu )\to \Delta (\lambda )\otimes \Delta (\mu ) be the canonical G G -morphism. We study the split condition for ι λ , μ \iota _{\lambda ,\mu } over Z ( p ) \mathbb {Z}_{(p)} , and apply this as an approach to compare the Jantzen filtrations of the Weyl modules Δ ( λ ) \Delta (\lambda ) and Δ ( λ + μ ) \Delta (\lambda +\mu ) . In the case when G G is of type A A , we show that the split condition is closely related to the product of certain Young symmetrizers and, under some mild conditions, is further characterized by the denominator of a certain Young’s seminormal basis vector. We obtain explicit formulas for the split condition in some cases.

Publisher

American Mathematical Society (AMS)

Subject

Mathematics (miscellaneous)

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Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. On the denominators of Young's seminormal basis;Journal of Combinatorial Theory, Series A;2022-10

2. Young's seminormal basis vectors and their denominators;Journal of Combinatorial Theory, Series A;2021-11

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