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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Cusp forms for reductive symmetric spaces of split rank one
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by Erik P. van den Ban and Job J. Kuit PDF
Represent. Theory 21 (2017), 467-533 Request permission

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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Additional 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