Let $G$ be a simple algebraic group and $P$ a parabolic subgroup of $G$ with abelian unipotent radical $P^u$, and let $B$ be a Borel subgroup of $G$ contained in $P$. Let $\mathfrak {p^u}$ be the Lie algebra of $P^u$ and $L$ a Levi factor of $P$. Then $L$ is a Hermitian symmetric subgroup of $G$ and $B$ acts with finitely many orbits both on $\mathfrak {p^u}$ and on $G/L$. In this paper we study the Bruhat order of the $B$\-orbits in $\mathfrak {p^u}$ and in $G/L$, proving respectively a conjecture of Panyushev and a conjecture of Richardson and Ryan.

厄米特对称簇和阿贝尔幂零根上的Bruhat序

雅各布·甘迪尼

安德雷亚·马菲

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