Representations of the exceptional Lie superalgebra E(3,6) II: Four seriesof degenerate modules

Four Z(+)-bigraded complexes with the action of the exceptional infinite-di mensional Lie superalgebra E(3,6) are constructed. We show that all the ima ges and cokernels and all but three kernels of the differentials are irredu cible E (3,6)-modules. This is based on the list of singular vectors and th e calculation of homology of these complexes. As a result, we obtain an exp licit construction of all degenerate irreducible E(3,6)-modules and compute their characters and sizes. Since the group of symmetries of the Standard Model SU(3) x SU(2) x U(1) (divided by a central subgroup of order six) is a maximal compact subgroup of the group of automorphisms of E(3,6), our res ults may have applications to particle physics.