The notion of cusp forms for a class of reductive symmetric spaces of   split rank one
  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. 
Erik P. van den Ban, Job J. Kuit and Henrik Schlichtkrull
math.RT