Formula for the computation of the representation matrix elements of the group S O (n)

Abstract

The formulas of expressing the infinitesimal operators of the parameter groups of SO (n) in terms of the Euler angles are given. By using these, recursion relations which are useful for calculations of the representation matrix elements of SO (n) are obtained. Expressions for the d functions with the highest and some weights are obtained explicitly, and it is shown that the d functions of SO (2j+1) or SO (2j) with special weights agree with those of SO (3) or SO (4) respectively. By using the results, a formula of computing the D−matrix elements of SO (n) are given in terms of lowering operators corresponding to those of Pang and Hecht.