S Theorem and Construction of the Invariants of the Semisimple Compact Lie Algebras

Abstract

An infinitesimal proof of the S theorem, which states that the invariants of a compact semisimple Lie algebra are symmetric with respect to the discrete Weyl group of the algebra, is given. The complete set of invariants of the various compact semisimple Lie algebras found by Racah are rederived in a somewhat different and explicit way, the S theorem being used to establish their completeness.