Translation functors for locally analytic representations

2021/07/18 by Akash Jena, Jena, Akash, Aranya Lahiri +2 · 1 citation
Mathematics · #11F85 #11S37 #17B10 #22E50 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2107.08493

openalex publication_date 2021/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a p-adic Lie group with reductive Lie algebra \mathfrakg. In analogy to the translation functors introduced by Bernstein and Gelfand on categories of U(\mathfrakg)-modules we consider similarly defined functors on the category of coadmissible modules over the locally analytic distribution algebra D(G) on which the center of U(\mathfrakg) acts locally finite. These functors induce equivalences between certain subcategories of the latter category. Furthermore, these translation functors are naturally related to those on category O via the functors from category O to the category of coadmissible modules. We also investigate the effect of the translation functors on locally analytic representations Π(V)^{\rm la} associated by the p-adic Langlands correspondence for \rm GL₂(ℚ_p) to 2-dimensional Galois representations V.

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• The functor \checkF^G_P at the level of K₀
• U(g)-finite locally analytic representations
• Solid locally analytic representations
• Duality for admissible locally analytic representations
• Towards the Derived Jacquet-Emerton Module Functor