广义扬岑过滤、双曲限制与特征闭链
Generalized Jantzen filtration, hyperbolic restriction, and characteristic cycles
中文总结 AI 辅助
本文以布拉登的双曲局部化函子为工具，刻画GLₙ(F)抛物诱导表示间解析intertwining算子的几何性质，证明其像半单并给出极点阶数下界，归约拉皮德与明格斯的相关猜想，混合霍奇模理论是证明关键。
中文摘要 AI 辅助
本文中，我们以布拉登的双曲局部化函子为工具，对局部非阿基米德域F上GLₙ(F)的抛物诱导表示之间的解析 intertwining 算子的行为给出几何描述。由此可证明 intertwining 算子的像恒为半单，并给出其极点阶数的下界，该下界被猜想与某类 perverse 层的奇异支集给出的上界相等。此外，我们能将拉皮德与明格斯关于诱导表示不可约子表示形态的猜想，归约为特征闭链的计算。混合霍奇模理论在证明中起到关键作用。
英文摘要
In this paper we give a geometric description of the behavior of analytic intertwining operators between parabolically induced representations of $\mathrm{GL}_n(\mathrm{F})$, where $\mathrm{F}$ is a local non-archimedean field, in terms of hyperbolic localization functors of Braden. As a consequence, we can show that the image of an intertwining operator is always semi-simple and give a lower bound on the order of its pole, which is conjectured to be an equality as well as an upper bound in terms of the singular support of certain perverse sheaves. Moreover, we are able to reduce the conjecture of Lapid and Mínguez on the shape of irreducible subrepresentations of induced representations to a computation of characteristic cycles. The theory of mixed Hodge modules plays a crucial role in the proofs.
