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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Generalized principal series representations
of $SL(1+n, \mathbb {C})$


Authors: Anthony H. Dooley and Genkai Zhang
Journal: Proc. Amer. Math. Soc. 125 (1997), 2779-2787
MSC (1991): Primary 22E46, 43A90
DOI: https://doi.org/10.1090/S0002-9939-97-03877-X
MathSciNet review: 1396975
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider certain induced representations of the group
$SL(n+1, \mathbb {C})$ realized on line bundles over the projective space of $\mathbb {C}^{n+1}$. We calculate the intertwining operators in the compact picture. We find all the unitarizable representations and determine the invariant norm.


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Additional Information

Anthony H. Dooley
Affiliation: School of Mathematics, University of New South Wales, Kensington, New South Wales 2033, Australia
Email: tony@solution.maths.unsw.edu.au

Genkai Zhang
Affiliation: Matematiska institutionen, Högskolan i Karlstad, S- 650 09 Karlstad, Sweden
Email: genkai.zhang@hks.se

DOI: https://doi.org/10.1090/S0002-9939-97-03877-X
Keywords: Representation, semisimple Lie group
Received by editor(s): September 26, 1995
Received by editor(s) in revised form: April 9, 1996
Additional Notes: Research sponsored by the Australian Research Council
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society