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Manuscript Title: Inner multiplicity of unitary groups.
Authors: S. Thomas, M.T. Sunny
Program title: IMUG
Catalogue identifier: AAAJ_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 14(1978)267
Programming language: Basic.
Computer: PDP-11/50.
Operating system: RSTS/E.
RAM: 4K words
Word size: 16
Peripherals: disc.
Keywords: General purpose, Lie algebra, Inner multiplicity, Unitary group, Gelfand pattern.
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:
There exists a rather simple method of calculating the inner multiplicity of weights of SU(n) by means of Gelfand patterns. The method of solution is given by Gruber and Delaney in their paper on classical groups and consists of counting all distinct Gelfand patterns which belong to the same weight.

Restrictions:
The program handles SU(n) groups with rank less than or equal to 9.

Unusual features:
Since the multiplicity of a particular weight in an irreducible representation is calculated without any references to other weights except the highest weight there is no restriction on the dimension of the representation. The program of Kolman and Beck is restricted in the dimension (fewer than 1000 weights). The program can also be used to obtain the various possible Gelfand patterns from a given partition.

Running time:
The multiplicity gamma(1,0,0,0,0,-1) = 5 in the representation D(2,0,0, 0,0,-2) is calculated in 3.6 s. 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 30.9 s.