PHYSICAL METHOD OF GROUP REPRESENTATION THEORY (IV)——THE IRREDUCIBLE BASES OF SUmn?SUm×SUn AND SUm+n?SUm?SUn

1 January 1978

journal article
Published by Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences in Acta Physica Sinica

Vol. 27 (2) , 203-218
https://doi.org/10.7498/aps.27.203

Abstract

It is proved that the CG coefficient of the permutation group and the outer-product reduction coefficient are just the coupling coefficient which couple the irreduci-ble basis of any SU(m) and SU(n), to those of SU(mn)?SU(m)× SU(n) and SU(m+n)?SU(m)?SU(n) respectively. Several simple methods are given for the calculation of the irreducible bases of SU(mn)?SU(m) × SU(n) and SU(m+n) ?SU(m)?SU(n) when using the Gelfand representation of SU(mn) and SU(m+n). The SU(6)?SU(3) × SU(2) and SU(8)?SU(4) × SU(2) baryon wave functions commonly used in elementary particle models are given in detail.

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