Multiplicity-free Wigner coefficients for semisimple Lie groups. II. A pattern calculus for O(n)

In this paper a direct, algebraic derivation of a large class of (multiplicity-free) reduced Wigner coefficients is presented for the orthogonal groups. In particular all elementary reduced Wigner coefficients, including those for the fundamental spinor and tensor representations, are obtained. The results are presented in a form directly analogous to the corresponding results obtained for the unitary groups.