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On Jordan-Hölder series of some locally analytic representations. (English) Zbl 1307.22009

Let \(G\) be a split reductive \(p\)-adic group. This paper is about the Jordan-Hölder series of locally analytic \(G\)-representations which are induced from locally algebraic representations of a parabolic subgroup \(P \subset G\). For every representation \(M\) of \(\mathrm{Lie}(G)\) in the BGG-category \(\mathfrak O\), which is equipped with an algebraic \(P\)-action, and for every smooth \(P\)-representation \(V\), the authors construct a locally analytic representation \(\mathcal{F}_P^G(M, V )\) of \(G\). This gives rise to a bi-functor to the category of locally analytic representations. It is proven that the bi-functor is exact, and a criterion for the topological irreducibility of \(\mathcal{F}_P^G(M, V )\) in terms of \(M\) and \(V\) is given. (BGG stands for Bernstein-Gelfand-Gelfand.)

MSC:

22E50 Representations of Lie and linear algebraic groups over local fields
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