The eigenvalues of the quadratic Casimir operator and second-order indices of a simple Lie algebra
نویسنده
چکیده
In these notes, we demonstrate how to compute the eigenvalue of the quadratic Casimir operator and the second-order index for an irreducible representation of a simple Lie algebra. Explicit results for the fundamental and adjoint representations of su(n), so(n) and sp(n) are given. The relation of these results to the dual Coxeter number is clarified. Finally, the dependence on the normalization of the Lie algebra generators is discussed.
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تاریخ انتشار 2013