---
_id: '64279'
abstract:
- lang: eng
  text: "<p>For reductive symmetric spaces <inline-formula content-type=\"math/mathml\">\r\n<mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G slash upper
    H\">\r\n  <mml:semantics>\r\n    <mml:mrow>\r\n      <mml:mi>G</mml:mi>\r\n      <mml:mrow
    class=\"MJX-TeXAtom-ORD\">\r\n        <mml:mo>/</mml:mo>\r\n      </mml:mrow>\r\n
    \     <mml:mi>H</mml:mi>\r\n    </mml:mrow>\r\n    <mml:annotation encoding=\"application/x-tex\">G/H</mml:annotation>\r\n
    \ </mml:semantics>\r\n</mml:math>\r\n</inline-formula> 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 <inline-formula content-type=\"math/mathml\">\r\n<mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G slash upper
    H\">\r\n  <mml:semantics>\r\n    <mml:mrow>\r\n      <mml:mi>G</mml:mi>\r\n      <mml:mrow
    class=\"MJX-TeXAtom-ORD\">\r\n        <mml:mo>/</mml:mo>\r\n      </mml:mrow>\r\n
    \     <mml:mi>H</mml:mi>\r\n    </mml:mrow>\r\n    <mml:annotation encoding=\"application/x-tex\">G/H</mml:annotation>\r\n
    \ </mml:semantics>\r\n</mml:math>\r\n</inline-formula>.</p>"
author:
- first_name: Erik
  full_name: van den Ban, Erik
  last_name: van den Ban
- first_name: Job
  full_name: Kuit, Job
  last_name: Kuit
citation:
  ama: van den Ban E, Kuit J. Cusp forms for reductive symmetric spaces of split rank
    one. <i>Representation Theory of the American Mathematical Society</i>. 2017;21(17):467-533.
    doi:<a href="https://doi.org/10.1090/ert/507">10.1090/ert/507</a>
  apa: van den Ban, E., &#38; Kuit, J. (2017). Cusp forms for reductive symmetric
    spaces of split rank one. <i>Representation Theory of the American Mathematical
    Society</i>, <i>21</i>(17), 467–533. <a href="https://doi.org/10.1090/ert/507">https://doi.org/10.1090/ert/507</a>
  bibtex: '@article{van den Ban_Kuit_2017, title={Cusp forms for reductive symmetric
    spaces of split rank one}, volume={21}, DOI={<a href="https://doi.org/10.1090/ert/507">10.1090/ert/507</a>},
    number={17}, journal={Representation Theory of the American Mathematical Society},
    publisher={American Mathematical Society (AMS)}, author={van den Ban, Erik and
    Kuit, Job}, year={2017}, pages={467–533} }'
  chicago: 'Ban, Erik van den, and Job Kuit. “Cusp Forms for Reductive Symmetric Spaces
    of Split Rank One.” <i>Representation Theory of the American Mathematical Society</i>
    21, no. 17 (2017): 467–533. <a href="https://doi.org/10.1090/ert/507">https://doi.org/10.1090/ert/507</a>.'
  ieee: 'E. van den Ban and J. Kuit, “Cusp forms for reductive symmetric spaces of
    split rank one,” <i>Representation Theory of the American Mathematical Society</i>,
    vol. 21, no. 17, pp. 467–533, 2017, doi: <a href="https://doi.org/10.1090/ert/507">10.1090/ert/507</a>.'
  mla: van den Ban, Erik, and Job Kuit. “Cusp Forms for Reductive Symmetric Spaces
    of Split Rank One.” <i>Representation Theory of the American Mathematical Society</i>,
    vol. 21, no. 17, American Mathematical Society (AMS), 2017, pp. 467–533, doi:<a
    href="https://doi.org/10.1090/ert/507">10.1090/ert/507</a>.
  short: E. van den Ban, J. Kuit, Representation Theory of the American Mathematical
    Society 21 (2017) 467–533.
date_created: 2026-02-19T13:31:09Z
date_updated: 2026-02-19T13:31:21Z
doi: 10.1090/ert/507
intvolume: '        21'
issue: '17'
language:
- iso: eng
page: 467-533
publication: Representation Theory of the American Mathematical Society
publication_identifier:
  issn:
  - 1088-4165
publication_status: published
publisher: American Mathematical Society (AMS)
status: public
title: Cusp forms for reductive symmetric spaces of split rank one
type: journal_article
user_id: '52730'
volume: 21
year: '2017'
...