Programs in Physics & Physical Chemistry
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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|
|Keywords: General purpose, Lie algebra, Inner multiplicity, Unitary groups, Gelfand patterns.|
Nature of problem:
To compute the inner multiplicity of a particular weight in a given representation for the special unitary groups using Gelfand patterns.
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.
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.
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.
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