Analysis of couplings with large tensor representations in SO(2N) and proton decay

We develop techniques for the analysis of SO(2N) invariant couplings which allow a full exhibition of the SU(N) invariant content of the spinor and te nser representations. The technique utilizes a basis consisting of a specif ic set of reducible SU(N) tensors in terms of which the SO(2N) invariant co uplings have a simple expansion. The technique is specially useful for coup lings involving large tenser representations. We exhibit the technique by p erforming a complete determination of the trilinear couplings in the superp otential for the case of SO(10) involving the 16 plet of matter, i.e., we g ive a full determination of the 16-16-10(s), 16-16-120(a) and 16-16-1 (2) o ver bar6(s) couplings. The possible role of large tenser representations in the generation of quark lepton textures is discussed. It is shown that the couplings involving 1 (2) over bar6-dimensional representation generate ex tra zeros in the Higgs tripler textures which can lead to an enhancement of the proton decay lifetime by a factor of 10(3). These results also have im plications for neutrino mass textures. (C) 2001 Published by Elsevier Scien ce B.V.