Complete cubic and quartic couplings of 16 and (16)-over-bar in SO(10) unification

A recently derived basic theorem on the decomposition of SO(2N) vertices is used to obtain a complete analytic determination of all SO(10)-invariant c ubic superpotential couplings involving 16(+/-) semispinors of SO(10) chira lity +/- and tensor representations. In addition to the superpotential coup lings computed previously using the basic theorem involving the 10, 120 and (126) over bar tensor representations we compute here couplings involving the 1-, 45- and 210-dimensional tensor representations, i.e., we compute th e (16) over bar (-/+) 16(+/-)1, (16) over bar (-/+) 16(+/-)45 and (16) over bar (-/+) 16(+/-)210 Higgs couplings in the superpotential. A complete det ermination of dimension five operators in the superpotential arising from t he mediation of the 1-, 45- and 210-dimensional representations is also giv en. The vector couplings (16) over bar (+/-)16(+/-)1, (16) over bar (+/-)16 (+/-)45 and (16) over bar (+/-)16(+/-)210 are also analyzed. The role of la rge tensor representations and the possible application of results derived here in model building are discussed. (C) 2001 Published by Elsevier Scienc e B.V.