The Calculation Of The Isoscalar Factors And The Clebsch-Gordan Coefficients Of Permutation Group S₇

With Eigenfunction Method,this work calculates the eigenfunctions of CSCO-I,CSCO-II of permutation groups.In addition,the isoscalar factors(ISF)and Clebsch-Gordan(CG)coefficients are calculated step by step.The results are given at the last of this paper,and the links of the data and the codes are also given.With the standard phase convention method of the absolute phases and the relative phases,the phase of the results are the same as Young-Yamanouchi phase convention,which widely used by academic world.Therefore,the results can be used directly by anyone without changing the phases.In this paper,three theorems were raised and proved individual.They are used in calculating Young-Yamanouchi bases’s phase;calculating Young tableaux index m;quickly calculating relative phase in ISF and CGC.