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Intertwining operators for the generalized principal series on a symmetric $ R$-space


Author: Jean-Louis Clerc
Journal: Trans. Amer. Math. Soc. 367 (2015), 4423-4458
MSC (2010): Primary 22E45, 43A80
DOI: https://doi.org/10.1090/S0002-9947-2014-06327-7
Published electronically: September 4, 2014
MathSciNet review: 3324934
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Abstract: Three questions about the intertwining operators for the generalized principal series on a symmetric $ R$-space are solved: description of the functional kernel, both in the noncompact and in the compact picture, domain of convergence, and meromorphic continuation. A large use is made of the theory of positive Jordan triple systems. The meromorphic continuation of the intertwining integral is achieved via a Bernstein-Sato identity, and a precise description of the poles is obtained.


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Additional Information

Jean-Louis Clerc
Affiliation: Institut Elie Cartan, Université de Lorraine, 54506 Vandœuvre-lès-Nancy, France
Email: jean-louis.clerc@univ-lorraine.fr

DOI: https://doi.org/10.1090/S0002-9947-2014-06327-7
Received by editor(s): October 2, 2012
Received by editor(s) in revised form: October 11, 2013, and November 12, 2013
Published electronically: September 4, 2014
Article copyright: © Copyright 2014 American Mathematical Society