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

## Description

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... Title of program: UNTOU3 Catalogue Id: ABLJ_v1_0 Nature of problem U(N) -> U(3) plethysm, that is, finding the complete set of irreducible representations (irreps) of U(3) in specific irreps of U(N) where N=(n+1) (n+2)/2 for nonnegative integer n values. Versions of this program held in the CPC repository in Mendeley Data ABLJ_v1_0; UNTOU3; 10.1016/0010-4655(89)90024-6 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)