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Manuscript Title: Inner multiplicity of unitary groups - a modified version.
Authors: S. Thomas
Program title: IMUG1
Catalogue identifier: AAAJ_v2_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 44(1987)221
Programming language: Fortran.
Computer: HONEYWELL DPS 8.
Operating system: HONEYWELL-CP6, MICRO-MSDOS VER2.1.
Word size: 36
Peripherals: disc.
Keywords: General purpose, Lie algebra, Inner multiplicity, Unitary groups, Gelfand patterns.
Classification: 4.2.

Nature of problem:
To compute the inner multiplicity of a particular weight in a given representation for the special unitary groups using Gelfand patterns.

Solution method:
The inner multiplicity of a particular weight in a given representation, characterised by the highest weight, can be found by counting all distinct Gelfand patterns which belong to the same weight.

The program as implemented here can handle SU(n) groups with rank less than or equal to 29.

Unusual features:
There is no restriction on the dimension of the representation. Other programs have restriction on the dimension of the representation. This program can be easily modified for higher rank algebras by adding and modifying certain source statements which are marked by comment lines. This program can also be used to obtain the various possible Gelfand patterns from a given partition.

Running time:
The multiplicity Gamma(0,0,0,0,0)=5 is the representation D(1,1,0,-1,-1) is calculated in .31 s by Honeywell computer and in 20 s by the micro computer. The multiplicity Gamma(0,0,0,0,0,0,0,0,0,0)=90 in the representation D(1,1,1,1,0,0,-1,-1,-1,-1) is calculated in 1.6 s by Honeywell computer and 295 s by the micro computer. As expected if the multiplicity is a large number it takes more time to calculate it. The third example for n=30 given below took .5 s by the mainframe computer and 75 s by the micro.