论文标题
还原群的球面典范
Spherical birational sheets in reductive groups
论文作者
论文摘要
我们将球形杂志纸分类为一个复杂的简单简单连接的代数组。我们使用分类表明，当$ g $是一个连接的还原复杂的代数群时，具有简单连接的派生子组，两个共轭类$ \ Mathcal {o} _1 $，$ \ nathcal {o} _2 $ g $ $ g $的$ g $在同一birational exprient to $ g中，以及仅由$ g的转移，以及仅在$ g中，仅在$ g中。 $ \ MATHCAL {O} _1 $和$ \ MATHCAL {O} _2 $是同构为$ G $ -MODULES。结果，我们证明了$ g $的Lie代数的球形子变量的猜想。
We classify the spherical birational sheets in a complex simple simply-connected algebraic group. We use the classification to show that, when $G$ is a connected reductive complex algebraic group with simply-connected derived subgroup, two conjugacy classes $\mathcal{O}_1$, $\mathcal{O}_2$ of $G$ lie in the same birational sheet, up to a shift by a central element of $G$, if and only if the coordinate rings of $\mathcal{O}_1$ and $\mathcal{O}_2$ are isomorphic as $G$-modules. As a consequence, we prove a conjecture of Losev for the spherical subvariety of the Lie algebra of $G$.
