$U (\mathfrak {g})$-finite locally analytic representations
Authors:
P. Schneider, J. Teitelbaum and Dipendra Prasad
Journal:
Represent. Theory 5 (2001), 111-128
MSC (2000):
Primary 17B15, 22D12, 22D15, 22D30, 22E50
DOI:
https://doi.org/10.1090/S1088-4165-01-00109-1
Published electronically:
May 18, 2001
MathSciNet review:
1835001
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Abstract | References | Similar Articles | Additional Information
Abstract: 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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Additional Information
P. Schneider
Affiliation:
Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Einsteinstr. 62, D-48149 Münster, Germany
MR Author ID:
156590
Email:
pschnei@math.uni-muenster.de
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:
jeremy@math.uic.edu
Dipendra Prasad
Affiliation:
Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad, 211019, India
MR Author ID:
291342
Email:
dprasad@mri.ernet.in
Received by editor(s):
August 2, 2000
Received by editor(s) in revised form:
September 25, 2000
Published electronically:
May 18, 2001
Article copyright:
© Copyright 2001
American Mathematical Society