Let $\mathfrak{g}$ be a complex semisimple Lie algebra, $G$ a simplyconnected and connected Lie group with Lie algebra $\mathfrak{g}$ and $V$ afinite dimensional representation. We prove that the zero locus of quadricscontaining $G.y$ is an irreducible variety in $\PP V$.
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机译:假设$ \ mathfrak {g} $是一个复杂的半简单Lie代数,$ G $是一个具有Lie代数$ \ mathfrak {g} $和$ V $的无穷维表示的简单连通的Lie群。我们证明了包含$ G.y $的二次曲面的零轨迹在$ \ PP V $中是不可约的。
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