The notion of cusp forms for a class of reductive symmetric spaces of split rank 1

TY - JOUR

T1 - The notion of cusp forms for a class of reductive symmetric spaces of split rank 1

AU - van den Ban, Erik P.

AU - Kuit, Job J.

AU - Schlichtkrull, Henrik

PY - 2019

Y1 - 2019

N2 - We study a notion of cusp forms for the symmetric spaces G/H with G = SL(n, R) and H = S(GL(n − 1, R) × GL(1, R)). We classify all minimal parabolic subgroups of G for which the associated cuspidal integrals are convergent and discuss the possible definitions of cusp forms. Finally, we show that the closure of the direct sum of the discrete series representations of G/H coincides with the space of cusp forms.

AB - We study a notion of cusp forms for the symmetric spaces G/H with G = SL(n, R) and H = S(GL(n − 1, R) × GL(1, R)). We classify all minimal parabolic subgroups of G for which the associated cuspidal integrals are convergent and discuss the possible definitions of cusp forms. Finally, we show that the closure of the direct sum of the discrete series representations of G/H coincides with the space of cusp forms.

UR - http://www.scopus.com/inward/record.url?scp=85069659429&partnerID=8YFLogxK

U2 - 10.1215/21562261-2019-0015

DO - 10.1215/21562261-2019-0015

M3 - Journal article

AN - SCOPUS:85069659429

SN - 0023-608X

VL - 59

SP - 471

EP - 513

JO - Kyoto Journal of Mathematics

JF - Kyoto Journal of Mathematics

IS - 2

ER -