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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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On Jordan-Hölder series of some locally analytic representations
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by Sascha Orlik and Matthias Strauch PDF
J. Amer. Math. Soc. 28 (2015), 99-157 Request permission

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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Additional Information
  • Sascha Orlik
  • Affiliation: Fachbereich C - Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Gaußstraße 20, D-42119 Wuppertal, Germany
  • Email: orlik@math.uni-wuppertal.de
  • Matthias Strauch
  • Affiliation: Indiana University, Department of Mathematics, Rawles Hall, Bloomington, Indiana 47405
  • MR Author ID: 620508
  • Email: mstrauch@indiana.edu
  • Received by editor(s): February 13, 2013
  • Received by editor(s) in revised form: December 4, 2013, and December 17, 2013
  • Published electronically: July 2, 2014
  • Additional Notes: M. S. would like to acknowledge the support of the National Science Foundation (award numbers DMS-0902103 and DMS-1202303).
  • © Copyright 2014 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 28 (2015), 99-157
  • MSC (2010): Primary 22E50, 11S37, 22E35; Secondary 20G05, 20G25, 17B35, 17B15
  • DOI: https://doi.org/10.1090/S0894-0347-2014-00803-1
  • MathSciNet review: 3264764