The dual group of a spherical variety
The dual group of a spherical variety
复制标题
球簇的对偶群
DOI：
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发表时间：
2017
期刊：
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通讯作者：
B. Schalke
中科院分区：
文献类型：
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作者：
F. Knop;B. Schalke
设$X$是连通约化群$G$的球变体。Gaitsgory-Nadler的工作有力地证明了$G$的Langlands对偶群$G^\vee$有一个子群，其Weyl群是$X$的小Weyl群。Sakellaridis-Venkatesh定义了一个精化的对偶群$G^\vee_X$，并在许多情况下证明了从$G^\vee_X$到$G^\vee$之间存在一个同生$\phi$。本文给出了$\phi$的完全一般存在性。我们的方法是纯组合的，并且适用于任意的$G$-变量（尽管标题是这样）。
Let $X$ be a spherical variety for a connected reductive group $G$. Work of Gaitsgory-Nadler strongly suggests that the Langlands dual group $G^\vee$ of $G$ has a subgroup whose Weyl group is the little Weyl group of $X$. Sakellaridis-Venkatesh defined a refined dual group $G^\vee_X$ and verified in many cases that there exists an isogeny $\phi$ from $G^\vee_X$ to $G^\vee$. In this paper, we establish the existence of $\phi$ in full generality. Our approach is purely combinatorial and works (despite the title) for arbitrary $G$-varieties.