[{"language":[{"iso":"eng"}],"doi":"10.1090/ert/507","title":"Cusp forms for reductive symmetric spaces of split rank one","year":"2017","publication_identifier":{"issn":["1088-4165"]},"author":[{"first_name":"Erik","last_name":"van den Ban","full_name":"van den Ban, Erik"},{"full_name":"Kuit, Job","first_name":"Job","last_name":"Kuit"}],"date_updated":"2026-02-19T13:31:21Z","publication_status":"published","intvolume":"        21","date_created":"2026-02-19T13:31:09Z","type":"journal_article","publication":"Representation Theory of the American Mathematical Society","issue":"17","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>"}],"page":"467-533","publisher":"American Mathematical Society (AMS)","_id":"64279","user_id":"52730","volume":21,"status":"public","citation":{"short":"E. van den Ban, J. Kuit, Representation Theory of the American Mathematical Society 21 (2017) 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>.","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} }","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>","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>."}}]