论文标题
在扩展的体重上，球形均匀空间
On extended weight monoids of spherical homogeneous spaces
论文作者
论文摘要
鉴于连接的还原复合体代数$ g $和球形子组$ h \ subset g $，扩展的重量himoid $ \widehatλ^+_ g（g/h）$编码$ g $ mmodule结构在所有$ g $ g $ linearized linearearized linearearized linearearized lineareareareal eareareareareal Areareareal in $ g/h $ g/h $ h $ $ g/h $的空间上。假设$ g $是半完整的，并且简单地连接，并且$ h $由定期嵌入抛物线子组$ p \ subset g $指定，在本文中，我们获得了$ \wideHatλ^+_ g（g/h）$的描述，通过$ g/h $的简单球根与某些combinator $ expical $ expically compace compace compace ncipectectionally nm \ widehatλ^+_ g（g/h）$（g/h）$（g/h）$。作为一个应用程序，我们推断出Avdeev和Gorfinkel结果的新证明，描述了$ \wideHatλ^+_ g（g/h）$在$ h $可解决的情况下。
Given a connected reductive complex algebraic group $G$ and a spherical subgroup $H \subset G$, the extended weight monoid $\widehat Λ^+_G(G/H)$ encodes the $G$-module structures on spaces of global sections of all $G$-linearized line bundles on $G/H$. Assuming that $G$ is semisimple and simply connected and $H$ is specified by a regular embedding in a parabolic subgroup $P \subset G$, in this paper we obtain a description of $\widehat Λ^+_G(G/H)$ via the set of simple spherical roots of $G/H$ together with certain combinatorial data explicitly computed from the pair $(P,H)$. As an application, we deduce a new proof of a result of Avdeev and Gorfinkel describing $\widehat Λ^+_G(G/H)$ in the case where $H$ is strongly solvable.
