Remote Access Representation Theory
Green Open Access

Representation Theory

ISSN 1088-4165



On the irreducibility of locally analytic principal series representations

Authors: Sascha Orlik and Matthias Strauch
Journal: Represent. Theory 14 (2010), 713-746
MSC (2010): Primary 22E50
Published electronically: December 1, 2010
MathSciNet review: 2738585
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: 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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2010): 22E50

Retrieve articles in all journals with MSC (2010): 22E50

Additional Information

Sascha Orlik
Affiliation: Fachgruppe Mathematik and Informatik, Bergische Universität Wuppertal, Gaußtraße 20, 42097 Wuppertal, Germany

Matthias Strauch
Affiliation: Department of Mathematics, Indiana University, 831 East Third Street, Bloomington, Indiana 47401

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.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.