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Manuscript Title: Representations of U(3) in U(N).
Authors: J.P. Draayer, Y. Leschber, S.C. Park, R. Lopez
Program title: UNTOU3
Catalogue identifier: ABLJ_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 56(1989)279
Programming language: Fortran.
Computer: IBM 3090/600E.
Operating system: MVS/XA-311, VMS 4.5.
RAM: 231K words
Word size: 32
Keywords: General purpose, Algebras, Harmonic oscillator, Three-dimensional Oscillator, Elliott su(3) scheme, Symplectic shell model, Microscopic collective Model, U(3) symmetry, Algebraic theory, Dynamical symmetry, U(n) -> u(3), Unitary group plethysm, Nuclear physics, Fractional parentage.
Classification: 4.2, 17.18.

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.

Solution method:
Solutions are obtained by applying a simple difference algorithm to the U(3) weight distribution function. The latter is generated in three steps: 1) by indentifying the N levels of U(N) as the distinguishable arrangements of n oscillator quanta in three cartesian directions, 2) by distributing the total number of qaunta (n * m if m is the number of valence particles) among these levels subject to restrictions (betweeness conditions) of the Gelfand scheme for labeling basis states of U(N), and 3) by summing over all the N levels to determine the final distribution of quanta in the three cartesian directions.

The main limitation is CPU time, see below. Storage can be a problem but the time constraint usually sets in long before program size becomes a problem. A PC with 640K of memory is sufficient to run most cases of interest in nuclear physics.

Unusual features:
Return codes set in the subprograms are used to fix branch points in the calling program. This modus operandi is implemented as a way of mocking-up recursive subprogram calls which is forbidden in FORTRAN but not, for example, in PASCAL.

Running time:
Execution times increase approximately linearly with d, the dimension of the irrep, and expotentially with n, the number of oscillator quanta. That is, t(cpu) ^ ( Alpha d) * exp(Beta n) where the constants Alpha and Beta are arround 13 * 10**-7 sec and 2.4 on the VAX 11/750 and 0.7 * 10**-7 sec and 2.6 on the IBM 3090/E, respectively.