The Clebsch–Gordan coefficients of S n

Abstract

Ordering schemes for the frames and tableaux of S_n are presented, and some results, expressible in terms of these, are developed. A formula is derived for the sign function on tableaux. A table of the nonzero Clebsch–Gordon coefficients for the ’’working triplets’’ is given. Methods are described, and a needed table supplied, for finding the other coefficients from the tabulated ones. The values are for n=2,...,6, with the coefficients for n=6 relegated to PAPS.