The characteristic identities and reduced matrix elements of the unitary and orthogonal groups

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Abstract
Polynomial identities satisfied by the generators of the Lie groups O(n) and U(n) are rederived. Using these identities the reduced matrix elements of the Lie groups U(n) and O(n) are evaluated as rational functions of the IR labels occurring in the canonical chains This method does not require an explicit realization of the Lie algebras and their representations using bosons. Finally, trace formulae encountered previously by several authors for finite dimensional irreducible representations are shown to hold on arbitrary representations admitting an infinitesimal character.

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