Please use this identifier to cite or link to this item: https://scholarbank.nus.edu.sg/handle/10635/155231
Title: Jantzen filtration of Weyl modules, product of Young symmetrizers and denominator of Young's seminormal basis
Authors: Fang, Ming
Lim, Kay Jin 
Tan, Kai Meng 
Keywords: math.RT
math.RT
20G05, 20C30
Issue Date: 2019
Citation: Fang, Ming, Lim, Kay Jin, Tan, Kai Meng (2019). Jantzen filtration of Weyl modules, product of Young symmetrizers and denominator of Young's seminormal basis. ScholarBank@NUS Repository.
Abstract: Let $G$ be a connected reductive algebraic group over an algebraically closed field of characteristic $p>0$, $\Delta(\lambda)$ denote the Weyl module of $G$ of highest weight $\lambda$ and $\iota_{\lambda,\mu}:\Delta(\lambda+\mu)\to \Delta(\lambda)\otimes\Delta(\mu)$ be the canonical $G$-morphism. We study the split condition for $\iota_{\lambda,\mu}$ over $\mathbb{Z}_{(p)}$, and apply this as an approach to compare the Jantzen filtrations of the Weyl modules $\Delta(\lambda)$ and $\Delta(\lambda+\mu)$. In the case when $G$ is of type $A$, we show that the split condition is closely related to the product of certain Young symmetrizers and is further characterized by the denominator of a certain Young's seminormal basis vector in certain cases. We obtain explicit formulas for the split condition in some cases.
URI: https://scholarbank.nus.edu.sg/handle/10635/155231
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