Characteristic Identities for Generators of <i>GL(n), O(n)</i> and <i>Sp(n)</i>

Abstract

A hierarchy of tensor identities, satisfied by the generators of the general linear group GL(n), is obtained in terms of two different sets of invariants. An application to the identification of irreducible representations and the decomposition of reducible representations is described. Similar results are obtained for the generators of orthogonal, pseudo-orthogonal, and symplectic groups.