A six-dimensional oscillator basis classified by O(6)⊇S𝒪(2)×S𝒰(3)⊇SO(3)

Abstract
We explicitly construct a complete set of states, useful in three-body problems, both in a boson operator realization and in terms of coordinates which are of interest to microscopic collective models. The states carry the angular momentum quantum number L and, for the classification scheme mentioned in the title, our expressions generalize to arbitrary L the results previously available only for L=0 and 1.