This project is maintained by ysykimura
2019年6月25日(火) 17:30~19:00
I-siteなんば 2F S1 (I-siteなんばへは，地下鉄御堂筋線大国町駅が最寄りです．)
Kai Meng Tan (National University of Singapore)
Jantzen filtration, Young symmetrizers, and Young’s seminormal basis
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 $\iota_{\lambda,\mu} : \Delta(\lambda + \mu) → \Delta(\lambda) \otimes \Delta(\mu)$ be the canonical $G$-morphism. We study the split condition for $\iota_{\lambda,\mu}$ over $Z_{(p)}$, 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.