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 -