New expressions for the eigenvalues of the invariant operators of the general linear and the orthosymplectic Lie superalgebras

We obtain expansions for the eigenvalues C/sub p/ of the invariant operators (Casimir operators) of the general linear, and the orthosymplectic Lie superalgebras in terms of products of suitably defined graded power sums P/sub k/. The resulting expressions are closed and provide unified formulas for computing the C/sub p/'s for those superalgebras as well as their corresponding Lie algebras. The formulas are remarkably simple to suggest that the power sums used in this text could play a more basic role in the understanding of the pattern of the expansion coefficients. Explicit illustrations are given for the various series for p< or =8