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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
Posted:
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
Email:
nwallach@ucsd.edu
DOI:
http://dx.doi.org/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
Article copyright:
© Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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