Generating functions for the eigenvalues of the Casimir operators of the orthogonal and symplectic groups

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Abstract
By constructing the appropriate generating functions, the eigenvalues of the Casimir operators for the orthogonal and the symplectic groups are expressed in terms of power sums which are formally the same for the O(2n), Sp(2n), O(2n+1) groups as for the U(n) groups. The results for the O(2n), Sp(2n), and the O(2n+1) groups are written as the corresponding results for the U(n) groups plus very simple correction terms. This approach unifies the treatment of the problem for the semisimple Lie groups. Explicit evaluation of the eigenvalues of the Casimir operators becomes very simple.

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