Representations of the Exceptional Lie superalgebra $E(3,6): II. Four series of degenerate modules

Details Representations of the Exceptional Lie superalgebra $E(3,6): II. Four series of degenerate modules Representations of the Exceptional Lie superalgebra $E(3,6): II. Four series of degenerate modules

2000-12-28

arxiv.org/abs/math-ph/0012050v1

Physics

Mathematical Physics

43 pages, LaTex

Scientific paper

10.1007/PL00005581

Four $\ZZ_+$-bigraded complexes with the action of the exceptional infinite-dimensional Lie superalgebra E(3,6) are constructed. We show that all the images and cokernels and all but three kernels of the differentials are irreducible E(3,6)-modules. This is based on the list of singular vectors and the calculation of homology of these complexes. As a result, we obtain an explicit construction of all degenerate irreducible E(3,6)-modules and compute their characters and sizes. Since the group of symmetries of the Standard Model $SU(3) \times SU(2) \times U(1)$ (divided by a central subgroup of order six) is a maximal compact subgroup of the group of automorphisms of E(3,6), our results may have applications to particle physics.

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