Representations of the Orthogonal Group. I. Lowering and Raising Operators of the Orthogonal Group and Matrix Elements of the Generators

Abstract

A parallel method to that of Pang and Hecht for the construction of normalized lowering and raising operators for the orthogonal group $\text{O(n)⊃O(n−1)⊃…⊃O(2)}$ is presented. The generators are defined in a slightly different way from those of Pang and Hecht, and the lowering and raising operators are constructed without using graphs. The Gel'fand‐Zetlin matrix elements of the infinitesimal generators of O(n) have also been obtained.