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Holomorphic continuation of generalized Jacquet integrals for degenerate principal series

Author(s): Nolan R. Wallach
Journal: Represent. Theory 10 (2006), 380-398.
MSC (2000): Primary 22E30, 22E45
Posted: September 29, 2006
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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
Email: nwallach@ucsd.edu

DOI: 10.1090/S1088-4165-06-00231-7
PII: S 1088-4165(06)00231-7
Received by editor(s): February 18, 2004 and, in final revised form, June 27, 2006
Posted: September 29, 2006
Additional Notes: The author was supported in part by an NSF Grant
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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