Canonical Root Vectors of SUn

Abstract

The present paper extends the study of SU_n to the determination of particular root vectors and fundamental weights. The root vectors are chosen so as to show explicitly the canonical nesting of subgroups SU_n$\supset$ SU_n−1 × U₁, SU_n−1$\supset$ SU_n−2 × U₁, etc. Explicit matrix representations of the fundamental representations are given. The results are all dependent upon the use of n vectors which define the fundamental region of SU_n. Eigenvalues of fundamental invariant operators are also given in terms of these n vectors.