K-invariant cusp forms for reductive symmetric spaces of split rank one

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Standard

K-invariant cusp forms for reductive symmetric spaces of split rank one. / Ban van den, Erik; Kuit, Job Jacob; Schlichtkrull, Henrik.

I: Forum Mathematicum, Bind 31, Nr. 2, 2019, s. 341-349.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Ban van den, E, Kuit, JJ & Schlichtkrull, H 2019, 'K-invariant cusp forms for reductive symmetric spaces of split rank one', Forum Mathematicum, bind 31, nr. 2, s. 341-349. https://doi.org/10.1515/forum-2018-0150

APA

Ban van den, E., Kuit, J. J., & Schlichtkrull, H. (2019). K-invariant cusp forms for reductive symmetric spaces of split rank one. Forum Mathematicum, 31(2), 341-349. https://doi.org/10.1515/forum-2018-0150

Vancouver

Ban van den E, Kuit JJ, Schlichtkrull H. K-invariant cusp forms for reductive symmetric spaces of split rank one. Forum Mathematicum. 2019;31(2):341-349. https://doi.org/10.1515/forum-2018-0150

Author

Ban van den, Erik ; Kuit, Job Jacob ; Schlichtkrull, Henrik. / K-invariant cusp forms for reductive symmetric spaces of split rank one. I: Forum Mathematicum. 2019 ; Bind 31, Nr. 2. s. 341-349.

Bibtex

@article{5abe326a4f2d4979a8d2ce7e40aee175,
title = "K-invariant cusp forms for reductive symmetric spaces of split rank one",
abstract = "Let G/H be a reductive symmetric space of split rank one and let K be a maximal compact subgroup of G. In a previous article the first two authors introduced a notion of cusp forms for G/H. We show that the space of cusp forms coincides with the closure of the space of K-finite generalized matrix coefficients of discrete series representations if and only if there exist no K-spherical discrete series representations. Moreover, we prove that every K-spherical discrete series representation occurs with multiplicity one in the Plancherel decomposition of G/H. ",
author = "{Ban van den}, Erik and Kuit, {Job Jacob} and Henrik Schlichtkrull",
year = "2019",
doi = "10.1515/forum-2018-0150",
language = "English",
volume = "31",
pages = "341--349",
journal = "Forum Mathematicum",
issn = "0933-7741",
publisher = "Walterde Gruyter GmbH",
number = "2",

}

RIS

TY - JOUR

T1 - K-invariant cusp forms for reductive symmetric spaces of split rank one

AU - Ban van den, Erik

AU - Kuit, Job Jacob

AU - Schlichtkrull, Henrik

PY - 2019

Y1 - 2019

N2 - Let G/H be a reductive symmetric space of split rank one and let K be a maximal compact subgroup of G. In a previous article the first two authors introduced a notion of cusp forms for G/H. We show that the space of cusp forms coincides with the closure of the space of K-finite generalized matrix coefficients of discrete series representations if and only if there exist no K-spherical discrete series representations. Moreover, we prove that every K-spherical discrete series representation occurs with multiplicity one in the Plancherel decomposition of G/H.

AB - Let G/H be a reductive symmetric space of split rank one and let K be a maximal compact subgroup of G. In a previous article the first two authors introduced a notion of cusp forms for G/H. We show that the space of cusp forms coincides with the closure of the space of K-finite generalized matrix coefficients of discrete series representations if and only if there exist no K-spherical discrete series representations. Moreover, we prove that every K-spherical discrete series representation occurs with multiplicity one in the Plancherel decomposition of G/H.

U2 - 10.1515/forum-2018-0150

DO - 10.1515/forum-2018-0150

M3 - Journal article

VL - 31

SP - 341

EP - 349

JO - Forum Mathematicum

JF - Forum Mathematicum

SN - 0933-7741

IS - 2

ER -

ID: 215037284