Abstract
Polynomial bases for the irreducible representations of the orthogonal group, which are characterized by the Gel'fand pattern, have been obtained. The method used is very similar to Moshinsky's and is a generalization from the unitary group to the orthogonal group. The Wigner coefficients of O(3), commonly called the Clebsch-Gordan coefficients of R(3), are rederived by means of the polynomial bases obtained in this paper.
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