Support varieties of baby Verma modules

发布时间：2018-06-06 作者：浏览次数：

Speaker:	姚裕丰教授	DateTime:	2018年6月8日(周五)下午5:00-6:00
Brief Introduction to Speaker: 姚裕丰教授，上海海事大学理学院。		Place:	六号楼二楼报告厅
Abstract:Let $G$ be a connected reductive algebraic group over an algebraically closed field $\textbf{k}$ of prime characteristic $p$ and $\ggg=\Lie(G)$. For a given nilpotent $p$-character $\chi\in\ggg^*$, let $Z_\chi(\lambda)$ be a baby Verma module associated with a restricted weight $\lambda$. A conjecture describing the support variety of $Z_\chi(\lambda)$ via that of its restricted counterpart is given: $\mathcal{V}_{\mathfrak{g}}(Z_\chi(\lambda))= \mathcal{V}_{\mathfrak{g}}(Z_0(\lambda))\cap \mathfrak{z}_{\mathfrak{g}}(\chi)$. Under the assumption of $p\geq h$(the Coxeter number) and $\lambda$ $p$-regular, this conjecture is proved when $\chi$ falls in the regular nilpotent orbit for any $\ggg$ and the sub-regular nilpotent orbit for $\ggg$ being of type $A_n$. We also verify this conjecture whenever $\ggg$ is of type $A_n$ and $\chi$ falls in the minimal nilpotent orbit. This is a joint work with Yi-Yang Li and Bin Shu.