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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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Additional Information

Nolan R. Wallach
Affiliation: Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0112
MR Author ID: 180225

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.