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Manuscript Title: Generation of the Clebsch-Gordan coefficients for Sn. | ||

Authors: S. Schindler, R. Mirman | ||

Program title: SYMCGM | ||

Catalogue identifier: ACXV_v1_0Distribution format: gz | ||

Journal reference: Comput. Phys. Commun. 15(1978)131 | ||

Programming language: Fortran. | ||

Computer: IBM 370/168. | ||

Operating system: OS/MVT/ASP. | ||

RAM: 252K words | ||

Word size: 8 | ||

Peripherals: magnetic tape. | ||

Keywords: General purpose, Symmetric group, Clebsch-Gordan coefficient, Tensor product, Decomposition, Irreducible Representation, Algebras. | ||

Classification: 4.2. | ||

Subprograms used: | ||

Cat
Id | Title | Reference |

ACXW_v1_0 | SYMFUNC | CPC 15(1978)147 |

Nature of problem:To find the decomposition of the tensor product of two irreducible representations of the symmetric group Sn (for any n) into a direct sum of irreducible representations, and to compute the matrices for the similarity transformations. | ||

Solution method:An iterative formula has been derived which gives the tensor coupling coefficients for Sn in terms of the Clesbsch-Gordan coefficients for Sn-1 and the matrix elements for the transposition (n-1n). The computation is then essentially by direct substitution. Symmetry relations are used to reduce the number of coefficients which need to be calculated. The Clebsch-Gordan coefficients are then found from the tensor coupling coefficients by methods previously developed. | ||

Restrictions:These are determined by the amount of storage space and running time allotted. For large n imprecision of the coefficients can be greater than their magnitude. The values of n for which the program works can be increased by using greater precision. If n is greater than 12 the integer format of the function FAC will have to be changed. With the values presently specified in the dimension statements the program will work for all n through 5 and in addition for all triplets for n=6. However, the larger triplets will have to be done individually. | ||

Unusual features:Since this is an iterative procedure the coefficients for Sn-1 must be stored for use in calculating those for Sn. This requires a large amount of storage. The program is designed to store only the non-zero coefficients. Symmetry properties allow the calculation and storage of only a subset of these. Thus, a large part of the program consists of search routines for finding coefficients. |

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