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
- MR Author ID: 180225
- Email: email@example.com
- 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
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
- Journal: Represent. Theory 10 (2006), 380-398
- MSC (2000): Primary 22E30, 22E45
- DOI: https://doi.org/10.1090/S1088-4165-06-00231-7
- MathSciNet review: 2266697