  Spectrum generating algebras are used in various fields of physics as models
to determine quantum structure, including energy levels and transition
strengths. The advantage of such models is that their group structure allows an
extensive understanding of the system being studied. In addition they possess a
simple classical limit, at least for bosonic systems. In this paper we discuss
an algebraic model of nuclear structure, the Interacting Boson Model (IBM), and
show that in one limit its group structure is particularly simple. For zero
angular momentum there is an effective lower dimensional group structure which
describes the system both classically and quantum mechanically.
