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 cubic superpotential couplings involving 16(+/-) semispinors of SO(10) chirality +/- and tensor representations. In addition to the superpotential couplings 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 the (16) over bar (-/+) 16(+/-)1, (16) over bar (-/+) 16(+/-)45 and (16) over bar (-/+) 16(+/-)210 Higgs couplings in the superpotential. A complete determination of dimension five operators in the superpotential arising from the mediation of the 1-, 45- and 210-dimensional representations is also given. 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 large tensor representations and the possible application of results derived here in model building are discussed. (C) 2001 Published by Elsevier Science B.V.