Equivariant Vector Bundles on the Drinfeld Upper Half Space over a Local Field of Positive Characteristic

2023/04/06 by Linden, Georg
#11F70 (Primary) #14G17 #14G22 #22E50 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2304.03166

Abstract

We describe the locally analytic 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 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^× with values in K-Banach algebras which are integral domains (resp. with values in finite extensions of K) in an appendix.

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