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Derived intertwining norms for reducible spherical principal series

Published online by Cambridge University Press:  09 April 2009

J. E. Gilbert
Affiliation:
Dept. Mathematics University of TexasAustin, Texas 78712USA e-mail: [email protected]
R. A. Kunze
Affiliation:
Dept. Mathematics University of GeorgiaAthens, Georgia 30602USA e-mail: [email protected]
C. Meaney
Affiliation:
School of MPCE Macquarie UniversityNSW 2109Australia e-mail [email protected]
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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).

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1996

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