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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 mathematics.

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

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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Locally analytic distributions and $p$-adic representation theory, with applications to $GL_{2}$
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by Peter Schneider and Jeremy Teitelbaum
J. Amer. Math. Soc. 15 (2002), 443-468
Published electronically: October 18, 2001


In this paper we study continuous representations of locally $L$-analytic groups $G$ in locally convex $K$-vector spaces, where $L$ is a finite extension of $\mathbb {Q}_p$ and $K$ is a spherically complete nonarchimedean extension field of $L$. The class of such representations includes both the smooth representations of Langlands theory and the finite dimensional algebraic representations of $G$, along with interesting new objects such as the action of $G$ on global sections of equivariant vector bundles on $p$-adic symmetric spaces. We introduce a restricted category of such representations that we call “strongly admissible” and we show that, when $G$ is compact, our category is anti-equivalent to a subcategory of the category of modules over the locally analytic distribution algebra of $G$. As an application we prove the topological irreducibility of generic members of the $p$-adic principal series for $GL_2(\mathbb {Q}_p)$. Our hope is that our definition of strongly admissible representation may be used as a foundation for a general theory of continuous $K$-valued representations of locally $L$-analytic groups.
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Bibliographic Information
  • Peter Schneider
  • Affiliation: Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Einsteinstr. 62, D-48149 Münster, Germany
  • MR Author ID: 156590
  • Email:
  • Jeremy Teitelbaum
  • Affiliation: Department of Mathematics, Statistics, and Computer Science (M/C 249), University of Illinois at Chicago, 851 S. Morgan St., Chicago, Illinois 60607
  • Email:
  • Received by editor(s): December 16, 1999
  • Received by editor(s) in revised form: May 16, 2001
  • Published electronically: October 18, 2001
  • © Copyright 2001 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 15 (2002), 443-468
  • MSC (2000): Primary 11S80, 22E50
  • DOI:
  • MathSciNet review: 1887640