  In a recent study[Phys. Rev. B 92 (2015) 125427], a hyperspherical approach
has been developed to study of few-body fractional quantum Hall states. This
method has been successfully applied to the exploration of few boson and
fermion problems in the quantum Hall region, as well as the study of
inter-Landau level collective excitations. However, the hyperspherical method
as it is normally implemented requires a subsidiary (anti-)symmetrization
process, which limits its computational effectiveness. The present work
overcomes these difficulties and extends the power of this method by
implementing a represen- tation of the hyperspherical many-body basis space in
terms of Slater determinants of single particle eigenfunctions. A clear
connection between the hyperspherical representation and the conventional
single particle picture is presented, along with a compact operator
representation of the theoretical framework.
