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Derived intertwining norms for reducible spherical principal series

Part of: Lie groups Abstract harmonic analysis

Published online by Cambridge University Press:  09 April 2009

J. E. Gilbert ,
R. A. Kunze  and
C. Meaney
J. E. Gilbert
Affiliation:
Dept. Mathematics University of TexasAustin, Texas 78712USA e-mail: gilbert@math.utexas.edu
R. A. Kunze
Affiliation:
Dept. Mathematics University of GeorgiaAthens, Georgia 30602USA e-mail: ray@joe.math.uga.edu
C. Meaney
Affiliation:
School of MPCE Macquarie UniversityNSW 2109Australia e-mail chrism@macadam.mpce.mq.edu.au
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Abstract

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We use the second derivative of intertwining operators to realize a unitary structure for the irreducible subrepresentations in the reducible spherical principal series of U(1, n). These representations can also be realized as the kernels of certain invariant first-order differential operators acting on sections of homogeneous bundles over the hyperboloid (U(1) × U(n))/U(1, n).

MSC classification

Secondary: 22E46: Semisimple Lie groups and their representations 22E30: Analysis on real and complex Lie groups 43A85: Analysis on homogeneous spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 61 , Issue 2 , October 1996 , pp. 171 - 188
Copyright
Copyright © Australian Mathematical Society 1996

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