Cusp forms for reductive symmetric spaces of split rank one
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- by Erik P. van den Ban and Job J. Kuit
- Represent. Theory 21 (2017), 467-533
- DOI: https://doi.org/10.1090/ert/507
- Published electronically: November 14, 2017
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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 $G/H$.References
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Bibliographic Information
- Erik P. van den Ban
- Affiliation: Mathematical Institute, Utrecht University, PO Box 80 010, 3508 TA Utrecht, The Netherlands
- MR Author ID: 30285
- Email: e.p.vandenban@uu.nl
- Job J. Kuit
- Affiliation: Institut für Mathematik, Universität Paderborn, Warburger Straße 100, 33089 Paderborn, Germany
- MR Author ID: 1015624
- Email: j.j.kuit@gmail.com
- 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.
- © Copyright 2017 American Mathematical Society
- Journal: Represent. Theory 21 (2017), 467-533
- MSC (2010): Primary 22E45, 43A85; Secondary 44A12
- DOI: https://doi.org/10.1090/ert/507
- MathSciNet review: 3723155