Geodesic
On Jordan-Hölder series of some locally analytic representations
Orlik, Sascha1 ; Strauch, Matthias2
1 Fachbereich C - Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Gaußstraße 20, D-42119 Wuppertal, Germany
2 Indiana University, Department of Mathematics, Rawles Hall, Bloomington, Indiana 47405
Journal of the American Mathematical Society, Tome 28 (2015) no. 1, pp. 99-157

Voir la notice de l'article provenant de la source American Mathematical Society

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 $V$.
DOI : 10.1090/S0894-0347-2014-00803-1

Orlik, Sascha 1 ; Strauch, Matthias 2

1 Fachbereich C - Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Gaußstraße 20, D-42119 Wuppertal, Germany
2 Indiana University, Department of Mathematics, Rawles Hall, Bloomington, Indiana 47405 
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Orlik, Sascha; Strauch, Matthias. On Jordan-Hölder series of some locally analytic representations. Journal of the American Mathematical Society, Tome 28 (2015) no. 1, pp. 99-157. doi: 10.1090/S0894-0347-2014-00803-1

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