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Manuscript Title: Generation of the Clebsch-Gordan coefficients for Sn.
Authors: S. Schindler, R. Mirman
Program title: SYMOR
Catalogue identifier: ACYH_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 15(1978)131
Programming language: Fortran.
Computer: IBM 370/168.
Operating system: OS/MVT/ASP.
RAM: 102K words
Word size: 8
Peripherals: magnetic tape.
Keywords: General purpose, Symmetric group, Orthonormality, Precision, Algebras.
Classification: 4.2.

Subprograms used:
Cat Id Title Reference
ACXV_v1_0 SYMCGM CPC 15(1978)131
ACXW_v1_0 SYMFUNC CPC 15(1978)147

Nature of problem:
The Clebsch-Gordan coefficients of the symmetric group obey certain orthonormality conditions. This program checks to see that the coefficients computed do actually obey to these conditions. The deviation from exact orthonormality also provides a useful estimate of the accuracy of the calculation and the precision of the coefficients. Note that the calculational procedure of SYMCGM does not force orthonormality, except to some extent, for multiplicity greater than one, for ro (=1).

Solution method:
The program is closely related to SYMCGM described in this paper and the notation and routines generally follow that program. Its input is the output of SYMCGM, and a single data card, similar to that for SYMCGM. For each triplet a vector is specified by a tableau index and a multiplicity index. All pairs of vectors in the triplet, are considered and the dot product for each pair calculated. The output is headed by value of n and the triplet indices. Then a line appears for each pair of vectors giving the trableau index for each vector, the multiplicity index for each, and then the value of the dot product. This dot product should be one if all the indices are the same and zero otherwise.

Any coefficient computed by SYMCGM can be checked.