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Representation Theory

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

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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On the irreducibility of locally analytic principal series representations
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by Sascha Orlik and Matthias Strauch PDF
Represent. Theory 14 (2010), 713-746 Request permission


Let $\mathbf {G}$ be a $p$-adic connected reductive group with Lie algebra $\mathfrak {g}$. For a parabolic subgroup $\mathbf {P} \subset \mathbf {G}$ and a finite-dimensional locally analytic representation $V$ of a Levi subgroup of $\mathbf {P}$, we study the induced locally analytic $\mathbf {G}$-representation $W = \operatorname {Ind}_{\mathbf {P}}^{\mathbf {G}}(V)$. Our result is the following criterion concerning the topological irreducibility of $W$: If the Verma module $U(\mathfrak {g}) \otimes _{U(\mathfrak {p})} V’$ associated to the dual representation $V’$ is irreducible, then $W$ is topologically irreducible as well.
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Additional Information
  • Sascha Orlik
  • Affiliation: Fachgruppe Mathematik and Informatik, Bergische Universität Wuppertal, Gaußtraße 20, 42097 Wuppertal, Germany
  • Email:
  • Matthias Strauch
  • Affiliation: Department of Mathematics, Indiana University, 831 East Third Street, Bloomington, Indiana 47401
  • MR Author ID: 620508
  • Email:
  • Received by editor(s): November 26, 2007
  • Received by editor(s) in revised form: March 16, 2010, and May 23, 2010
  • Published electronically: December 1, 2010
  • Additional Notes: M.S. is partially supported by NSF grant DMS-0902103.
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 14 (2010), 713-746
  • MSC (2010): Primary 22E50
  • DOI:
  • MathSciNet review: 2738585