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Representation Theory

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Cusp forms for reductive symmetric spaces of split rank one

Authors: Erik P. van den Ban and Job J. Kuit
Journal: Represent. Theory 21 (2017), 467-533
MSC (2010): Primary 22E45, 43A85; Secondary 44A12
Published electronically: November 14, 2017
MathSciNet review: 3723155
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Abstract: For reductive symmetric spaces $ G/H$ of split rank one we identify a class of minimal parabolic subgroups for which certain cuspidal integrals of Harish-Chandra-Schwartz functions are absolutely convergent. Using these integrals we introduce a notion of cusp forms and investigate its relation with representations of the discrete series for $ G/H$.

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Additional Information

Erik P. van den Ban
Affiliation: Mathematical Institute, Utrecht University, PO Box 80 010, 3508 TA Utrecht, The Netherlands

Job J. Kuit
Affiliation: Institut für Mathematik, Universität Paderborn, Warburger Straße 100, 33089 Paderborn, Germany

Received by editor(s): February 25, 2017
Received by editor(s) in revised form: August 28, 2017
Published electronically: November 14, 2017
Additional Notes: The second author was supported by the Danish National Research Foundation through the Centre for Symmetry and Deformation (DNRF92) and the ERC Advanced Investigators Grant HARG 268105.
Article copyright: © Copyright 2017 American Mathematical Society