The Functors F^G_P over Local Fields of Positive Characteristic

2024/07/09 by Georg Linden, Linden, Georg
Mathematics · #22E35 (Secondary) #22E50 (Primary) 20G25 #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #Representation Theory (math.RT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2407.06873

openalex publication_date 2024/07/09 · openalex created_date 2024/07/11 · openalex updated_date 2026/07/28

Abstract

Let G be a split connected reductive group over a non-archimedean local field. In the p-adic setting, Orlik-Strauch constructed functors from the BGG category O associated to the Lie algebra of G to the category of locally analytic representation of G. We generalize these functors to such groups over non-archimedean local fields of arbitrary characteristic. To this end, we introduce the hyperalgebra of a non-archimedean Lie group G, which generalizes its Lie algebra, and consider topological modules over the algebra of locally analytic distributions on G and subalgebras related to this hyperalgebra.

Related

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• Category \mathcal O and locally analytic representations
• On some properties of the functors \mathcal F^G_P from Lie algebra to locally analytic representations
• Translation functors for locally analytic representations
• Locally analytic distributions and p-adic representation theory, with applications to GL₂