Analysis of SO(2N) Couplings of Spinor and Tensor Representations in $SU(N)\times U(1)$ Invariant Forms

Abstract

A review is given of a recently developed technique for the analysis of SO(2N) invariant couplings which allows a full exhibition of the SU(N) invariant content of couplings involving the SO(2N) semi-spinors $|\Psi_{\pm}>$ with chiralilty $\pm$ and tensor representations. We discuss the Basic Theorem used in the analysis and then exhibit the technique by illustrative examples for the computation of the trilinear and quartic couplings for the SO(10) case involving three generations of 16 plets of matter.Comment: 8 pages Latex. Prepared for Proceedings of Pran Nath Fest in PASCOS04, August 17-22, 200