Direct evaluation of spin representation matrices and ordering of permutation-group elements

A direct and general method is presented for constructing the orthogonal spin representation matrices (irreps) of the permutation group corresponding to the Yammanouchi-Kotani coupling scheme. For arbitrary permutations the irreps are constructed directly from the Young tableaus by a process which is, in general, only quadratic in the number of spin eigenfunctions, but which in actual computations becomes linear on vector computers for moderate sizes of the matrices. We also introduce a graphical representation of the group elements and a universal lexical ordering of permutations. The methods have been implemented and computational examples are presented.