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

Author(s): Anthony H. Dooley; Genkai Zhang
Journal: Proc. Amer. Math. Soc. 125 (1997), 2779-2787.
MSC (1991): Primary 22E46, 43A90
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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, Hö{}gskolan i Karlstad, S- 650 09 Karlstad, Sweden
Email: genkai.zhang@hks.se

DOI: 10.1090/S0002-9939-97-03877-X
PII: S 0002-9939(97)03877-X
Keywords: Representation, semisimple Lie group
Received by editor(s): September 26, 1995 and, in revsied form, April 9, 1996
Additional Notes: Research sponsored by the Australian Research Council
Communicated by: Palle E. T. Jorgensen
Copyright of article: Copyright 1997, American Mathematical Society

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