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Manuscript Title: Racah's outer multiplicity formula.
Authors: R.E. Beck, B. Kolman
Program title: RACOUT
Catalogue identifier: AAAG_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 8(1974)95
Programming language: Fortran.
Computer: IBM 370/168.
Operating system: HASP-II.
RAM: 62K words
Word size: 16
Keywords: General purpose, Lie algebra, Outer multiplicity, Irreducible Representation, Racah's formula.
Classification: 4.2.

Subprograms used:
Cat Id Title Reference
AAAA_v1_0 FREUD CPC 6(1973)24

Nature of problem:
To find the decomposition of the tensor product of two irreducible representations of a complex simple Lie algebra into a direct sum of irreducible representations.

Solution method:
The weight diagram of the smaller dimensioned representation is generat- ed using Dynkin's algorithm and Freudenthal's formula. The highest weight of any irreducible component of the tensor product of the given representations with highest weights lambda' and lambda'' can be written as mu + lamba'' where mu is a member of the weight system of lambda' (assumed to be the smaller dimensioned representation). All sums mu+ lambda'' are formed and if mu+ lambda'' is dominant, Racah's formula is used to compute its outer multiplicity.

The program handles all Lie algebras of rank <= 9. The smaller dimensioned representation must have no more than 1000 weights.

Unusual features:
An efficient method of truncating the sum over the Weyl group is used so that only a small number of terms need be taken even when the Weyl group is used so that only a small number of terms need be taken even when the Weyl group has order greater than 10**6. 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 IBM 360 and 370 series, variables not beginning with I to N will have to be declared as type INTEGER.

Running time:
The first (ordered by dimension) ten nontrivial pairs of representations for the Lie algebra B3 ran in 1.2 s.