作用于树的群的尖点表示的类型与坍缩
Types and collapse for cuspidal representations of groups acting on trees
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中文总结 AI 辅助
本文针对作用于树的群的尖点表示，在之前秩一p进群超尖点表示的几何局部化方法基础上，通过几何极小K型描述诱导数据、证明等变层坍缩为内射层，将相关概念推广至高秩群并提出猜想。
中文摘要 AI 辅助
在之前的一篇论文中，第二作者证明了每个秩一p进群的超尖点表示都由一个模中心紧开子群诱导，该方法是几何的，通过将表示局部化以得到树上的等变层。本文在此基础上提供了两个改进：一是通过几何极小K型对诱导数据进行几何描述；二是证明等变层可坍缩为内射层。几何极小K型与可坍缩性这两个概念可推广到更高秩的群，进而引出一对猜想。
英文摘要
In a previous paper, the second author proved that every supercuspidal representation of a rank-one p-adic group is induced from a compact-mod-center open subgroup. The method was geometric, localizing representations to obtain equivariant sheaves on trees. Here we provide two refinements. The first is a geometric description of the inducing data, via a geometrically minimal K-type. Second is a proof that the equivariant sheaves collapse onto injective sheaves. The two notions of geometrically minimal K-types and collapsibility generalize to higher rank groups, suggesting a pair of conjectures.
