正特征局部域上Drinfeld上半空间上的等变向量丛
Equivariant Vector Bundles on the Drinfeld Upper Half Space over a Local Field of Positive Characteristic
AI总结：
本文将Orlik关于p-adic域的齐次向量丛整体截面工作推广至正特征局部域，通过子表示过滤和改编的函子刻画子商，并确定了K^×的局部解析与连续特征。
摘要：
我们描述了作为射影空间上齐次向量丛的整体截面出现的局部解析GL_d(K)-表示，该射影空间被限制在非阿基米德局部域K上的Drinfeld上半空间上。因此，我们将Orlik（2008）关于p-adic域的工作推广到正特征的局部域上。我们通过子表示的过滤来描述该整体截面空间，并通过改编Orlik-Strauch（2015）和Agrawal-Strauch（2022）考虑的函子F^G_P来刻画所得的子商。对于正特征的局部域K，我们在附录中还确定了K^×的取值于作为整环的K-Banach代数（分别取值于K的有限扩张）的局部解析（分别连续）特征。
英文摘要：
We describe the locally analytic $\mathrm{GL}_d(K)$-representations which arise as the global sections of homogeneous vector bundles on the projective space restricted to the Drinfeld upper half space over a non-archimedean local field $K$. We thereby generalize work of Orlik (2008) for $p$-adic fields to the effect that it becomes applicable to local fields of positive characteristic. Our description of this space of global sections is in terms of a filtration by subrepresentations, and a characterization of the resulting subquotients via adaptations of the functors $\mathcal{F}^G_P$ considered by Orlik-Strauch (2015) and Agrawal-Strauch (2022). For a local field $K$ of positive characteristic, we also determine the locally analytic (resp. continuous) characters of $K^\times$ with values in $K$-Banach algebras which are integral domains (resp. with values in finite extensions of $K$) in an appendix.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
