arXiv 2402.090172024-02-14math.RTmath.AG

Coxeter 型 $p$ 进 Deligne-Lusztig 概形的上同调

The cohomology of $p$-adic Deligne-Luszitg schemes of Coxeter type

Alexander B. Ivanov, Sian Nie

AI总结：

本文确定了局部非阿基米德域上 Coxeter 型 $p$-Deligne-Lusztig 概形闭 Drinfeld 层的上同调，证明环面权空间集中于单一上同调度数且为成对非同构不可约表示，并探讨了 Moy-Prasad 商的极大性与 Kirillov 轨道方法的关系。

摘要：

我们确定了局部非阿基米德域上非分歧群任意内形式所关联的 Coxeter 型 $p$-Deligne-Lusztig 概形的闭 Drinfeld 层的上同调。我们证明相应的环面权空间恰好支撑于单一上同调度数，并且是相应抛物子群的无幂根的成对非同构不可约表示。我们还证明了该层所有 Moy-Pradt 商是极大簇，并研究了所得表示与 Kirillov 轨道方法的关系。

英文摘要：

We determine the cohomology of the closed Drinfeld stratum of $p$-Deligne--Lusztig schemes of Coxeter type attached to arbitrary inner forms of unramified groups over a local non-archimedean field. We prove that the corresponding torus weight spaces are supported in exactly one cohomological degree, and are pairwisely non-isomorphic irreducible representations of the pro-unipotent radical of the corresponding parahoric subgroup. We also prove that all Moy--Prasad quotients of this stratum are maximal varieties, and we investigate the relation between the resulting representations and Kirillov's orbit method.

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