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Representation Theory

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Holomorphic continuation of generalized Jacquet integrals for degenerate principal series

Author: Nolan R. Wallach
Journal: Represent. Theory 10 (2006), 380-398
MSC (2000): Primary 22E30, 22E45
Published electronically: September 29, 2006
MathSciNet review: 2266697
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Abstract: This paper introduces a class of parabolic subgroups of real reductive groups (called ``very nice''). For these parabolic subgroups we study the generalized Whittaker vectors for their degenerate principal series. It is shown that there is a holomorphic continuation of the Jacquet integrals associated with generic characters of their unipotent radicals. Also, in this context an analogue of the ``multiplicity one'' theorem is proved. Included is a complete classification of these parabolic subgroups (due to K. Baur and the author). These parabolic subgroups include all known examples of such continuations and multiplicity theorems.

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Nolan R. Wallach
Affiliation: Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0112

Received by editor(s): February 18, 2004
Received by editor(s) in revised form: June 27, 2006
Published electronically: September 29, 2006
Additional Notes: The author was supported in part by an NSF Grant
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.