We show that any Weyl group orbit of weights for the Tannakian group of semisimple holonomic 𝒟 {{\mathscr{D}}} -modules on an abelian variety is realized by a Lagrangian cycle on the cotangent bundle. As applications we discuss a weak solution to the Schottky problem in genus five, an obstruction for the existence of summands of subvarieties on abelian varieties, and a criterion for the simplicity of the arising Lie algebras.

中文翻译：

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高斯图谱的特征周期和微局部几何，II

我们证明，在阿贝尔变种上，半简单完整nomic {{\ mathscr {D}}}-模块的Tannakian群的权重的任何Weyl群轨道都是通过切切束上的拉格朗日循环实现的。作为应用，我们讨论了第五类中对肖特基问题的弱解，对阿贝尔变体上亚变数和的存在性的阻碍以及对所产生的李代数的简单性的判据。