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Manuscript Title: Program for calculating SU(4) Clebsch-Gordan coefficients
Authors: Markus Kuhn, Hans Walliser
Program title: CGSU4
Catalogue identifier: AEBL_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 179(2008)733
Programming language: Fortran 95.
Computer: Personal Computer.
Operating system: Linux, Windows.
RAM: 2 MB
Keywords: SU(4), Clebsch-Gordan coefficients, Wigner coefficients, vector coupling coefficients, Isoscalar factors.
PACS: 02.20.Rt.
Classification: 4.2.

Subprograms used:
Cat Id Title Reference
ACRM_v1_0 SU(3) CPC 5(1973)405

Nature of problem:
The SU(4) Clebsch-Gordan coefficients according to the group chain SU(4) ⊃ SU(3) x U(1) ⊃ SU(2) x U(1) ⊃ U(1) are calculated for arbitrary couplings.

Solution method:
The eigenfunctions method in combination with recurrence relations is used to generate tables of the SU(4) ⊃ SU(3) x U(1) isoscalar factors for the decomposition {Na}⊗ {Nb} → {N}γ with the multiplicity label γ. The SU(4) Clebsch-Gordan coefficients are then composed by these isoscalar factors and SU(3) Clebsch-Gordan coefficients according to the Racah factorization lemma.

Restrictions:
The dimensions of the involved representations are limited by the size of the arrays defined in the program.

Additional comments:
If many Clebsch-Gordan coefficients are needed for the same decomposition {Na}⊗ {Nb} → {N}γ , the running time is significantly reduced if the table of isoscalar factors is calculated only once.
The SU(3) code [1] and the code for eigen, a matrix diagonalization program (IBM scientific subroutine package) are included in the CGSU4 code package.

Running time:
The running time sensitively depends on the specific Clebsch-Gordan decomposition and the dimensions of the involved representations, varying from parts of a second to a minute.

References:
[1] Y. Akiyama and J. P. Draayer, Comput. Phys. Commun. 5 (1973) 405