Spectrum generating algebra of the symmetric top

The study of few-body problems has played an important role in many areas of physics [1]. Over the years accurate methods have been developed to solve the few-body equations. The degree of sophistication required depends on the physical system, i.e. to solve the fewbody problem in atomic physics requires a far higher accuracy than in hadronic physics. In recent years the development and application of algebraic methods to the many-body problem (e.g. collective excitations in nuclei [2] and molecules [3]) has received considerable attention. In spectroscopic studies these algebraic methods provide a powerful tool to study symmetries and selection rules, to classify the basis states, and to calculate matrix elements. In this paper we discuss an application of algebraic methods to the few-body problem. Especially in the area of hadronic physics, which is that of strong interactions at low energies, for which exact solutions of QCD are unavailable, these methods may become very useful [4].