Invariant Operators of the Unitary Unimodular Group in n Dimensions

Abstract

An elementary derivation is given of Biedenharn's construction of a complete set of independent invariants for the group SU(n). The basic tool is the mapping of the adjoint representation onto the linear space of generators in the defining representation. The trace of any algebraic function of the matrix thus associated is seen to constitute an invariant of the adjoint representation and yields by substitution an invariant operator. The independent invariants are recognized by their isomorphy to the invariant forms under the permutation group.