# Representations of U(3) in U(N)

#### Abstract

An interactive FORTRAN code for determining the representations of U(3) that occur in a representation of U(N) is introduced. The U(N)→U(3) chain is the basic group structure of the isotropic oscillator in three dimensions. In particular, N = (n+1)(n+2)/2 is the degeneracy of the shell with n quanta per level. Since the oscillator potential is a good starting approximation for the self-consistent field that binds nucleons in the nucleus, motivation for the work comes from nuclear physics, and in particular, from studies of quadrupole collective phenomena in deformed nuclear systems. A PASCAL version of the program, which is simpler because the basic algorithm is a recursive one, is also available. © 1989.

*This paper has been withdrawn.*