On the Representations of the Semisimple Lie Groups. I. The Explicit Construction of Invariants for the Unimodular Unitary Group in N Dimensions

Abstract

It is intended in the present series of papers to discuss explicit constructive determinations of the representations of the semisimple Lie groups SUn by an extension of the Racah-Wigner techniques developed for the two-dimensional unimodular unitary group (SU2). The present paper defines, and explicitly determines, a symmetric vector-coupling coefficient for the group SUn. These coefficients are utilized to construct a series of canonical invariants for SUn, of which the first I2 is the familiar Casimir invariant, and it is proved (by construction) that these invariants form a complete system of independent invariants suitable for uniquely labeling the irreducible inequivalent representations of SUn.