On Jordan-Hölder series of some locally analytic representations

Orlik, Sascha; Strauch, Matthias

doi:10.1090/S0894-0347-2014-00803-1

On Jordan-Hölder series of some locally analytic representations
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by Sascha Orlik and Matthias Strauch;

J. Amer. Math. Soc. 28 (2015), 99-157

DOI: https://doi.org/10.1090/S0894-0347-2014-00803-1

Published electronically: July 2, 2014

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Abstract:

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 $P \subset G$. We construct for every representation $M$ of $\textrm {Lie}(G)$ in the BGG-category ${\mathcal O}$, which is equipped with an algebraic $P$-action, and for every smooth $P$-representation $V$, a locally analytic representation ${\mathcal F}^G_P(M,V)$ of $G$. This gives rise to a bi-functor to the category of locally analytic representations. We prove that it is exact and give a criterion for the topological irreducibility of ${\mathcal F}^G_P(M,V)$ in terms of $M$ and $V$.

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