TY - UNPB
T1 - The notion of cusp forms for a class of reductive symmetric spaces of split rank one
AU - van den Ban, E
AU - Kuit, Job
AU - Schlichtkrull, H.
PY - 2014/6/6
Y1 - 2014/6/6
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) x 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 of 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) x 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 of representations of G/H coincides with the space of cusp forms.
U2 - 10.48550/arXiv.1406.1634
DO - 10.48550/arXiv.1406.1634
M3 - Working paper
SP - 1
EP - 41
BT - The notion of cusp forms for a class of reductive symmetric spaces of split rank one
PB - arXiv
ER -