Construction of grand unified models under maximal subalgebras

A construction of grand unified models of the strong, weak and electromagnetic interactions is described based on the transformation properties of the group generators under a maximal subgroup decomposition without recourse to large representation matrices or to the specific algebraic structures of some classical Lie-groups, such as the Clifford algebra associated with the orthogonal groups or the octonionic structure of the exceptional groups. To illustrate the procedure an explicit construction is given of the SU(5) model useful in the discussion of higher rank groups, of SO(10) under the maximal subalgebras SU(2)L × SU(2)R × SU(4)c and SU(5) × U(1)r and of the exceptional group E6 under SU(3)L × SU(3)R × SU(3)c and SO(10) × U(1)t. The construction procedure can be used as well with any classical Lie-group. © 1984