Holomorphic continuation of generalized Jacquet integrals for degenerate principal series

Wallach, Nolan

doi:10.1090/S1088-4165-06-00231-7

Holomorphic continuation of generalized Jacquet integrals for degenerate principal series
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by Nolan R. Wallach

Represent. Theory 10 (2006), 380-398

DOI: https://doi.org/10.1090/S1088-4165-06-00231-7

Published electronically: 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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