报告地点：行健楼526
邀请人：陈慧斌博士
Abstract: Let $G$ be a connected complex Lie group, $(\rho,V)$ a finite dimensional complex representation of $G$. The triplet $(G,\rho,V)$ is called a prehomogeneous vector space if there exists in $V$ an open $G$-orbit, and if, in addition, $\dim G=\dim V$, the triple is call cuspidal. In this talk, we will present some results on the classification of cuspidal prehomogeneous vector spaces for reductive Lie groups and will explain the relationship between prehomogeneou vector spaces, flat $G$-invariant metrics, $G$-invariant symplectic structures, Rota-Baxter algebras, etc. This is joint work with Yang, Xiaomei.