A recursive method for the construction of irreducible representations of the orthogonal group O(n)

An algorithm for the construction of O(n) Gel'fand - Zetlin states in an invariant vector space is developed. The states are calculated recursively using a new type of coefficient of fractional parentage. These coefficients are the eigenvectors of the Gel'fand invariants. It is shown that the calculation of the Gel'fand invariants' matrix elements can be reduced to the evaluation of a single generator at each step. This algorithm provides, a new approach to the calculation of the Clebsh - Gordon coefficients and isoscalar factors for the orthogonal group and can be applied to construct a basis function with well-defined orthogonal symmetry for physical systems where separation between collective motions and intrinsic motions, associated with the group O(n), is of interest.