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Manuscript Title: Freudenthal's inner multiplicity formula.
Authors: B. Kolman, R.E. Beck
Program title: FREUD
Catalogue identifier: AAAA_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 6(1973)24
Programming language: Fortran.
Computer: IBM 360/165.
Operating system: HASP-II.
RAM: 46K words
Word size: 16
Keywords: General purpose, Lie algebra, Inner multiplicity, Representation, Freudenthal's formula, Character.
Classification: 4.2.

Nature of problem:
To compute the weight diagram of an irreducible representation rho of a complex simple Lie algebra. This problem is equivalent to computing the character of rho.

Solution method:
The weight system of the representation is generated using Dynkin's algorithm. Inner multiplicities of the dominant weights are computed using Freudenthal's formula. The multiplicities of the non-dominant weights are computed recursively using a method, based on Weyl reflections, of finding equivalent dominant weights.

Restrictions:
The program handles all Lie algebras of rank <= 9 and representations with fewer than 1,000 weights.

Unusual features:
Due to the use of Weyl reflections and emphasis on dominant weights, this implementation is more efficient. By removing the I/O, the program can be used as a subroutine in the computation of outer multiplicities. By using the IBM 360 Fortran IV IMPLICIT statement all variables in the program are declared to be integers. When running on computers other than the IBM 360 and 370 series variables not beginning with I to N will have to be declared as type INTEGER.

Running time:
F4, highest weight = 0100, 0.38 s; A3, highest weight = 030, 0.03 s.