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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

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$U (\mathfrak {g})$-finite locally analytic representations
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by P. Schneider, J. Teitelbaum and Dipendra Prasad
Represent. Theory 5 (2001), 111-128
Published electronically: May 18, 2001


In this paper we continue our algebraic approach to the study of locally analytic representations of a $p$-adic Lie group $G$ in vector spaces over a non-Archimedean complete field $K$. We characterize the smooth representations of Langlands theory which are contained in the new category. More generally, we completely determine the structure of the representations on which the universal enveloping algebra $U(\mathfrak g)$ of the Lie algebra $\mathfrak g$ of $G$ acts through a finite dimensional quotient. They are direct sums of tensor products of smooth and rational $G$-representations. Finally we analyze the reducible members of the principal series of the group $G=SL_2(\mathbb Q_p)$ in terms of such tensor products.
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Bibliographic Information
  • P. Schneider
  • Affiliation: Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Einsteinstr. 62, D-48149 Münster, Germany
  • MR Author ID: 156590
  • Email:
  • J. 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:
  • Dipendra Prasad
  • Affiliation: Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad, 211019, India
  • MR Author ID: 291342
  • Email:
  • Received by editor(s): August 2, 2000
  • Received by editor(s) in revised form: September 25, 2000
  • Published electronically: May 18, 2001
  • © Copyright 2001 American Mathematical Society
  • Journal: Represent. Theory 5 (2001), 111-128
  • MSC (2000): Primary 17B15, 22D12, 22D15, 22D30, 22E50
  • DOI:
  • MathSciNet review: 1835001