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Hypermatrix factors for string and membrane junctions
The adjoint representations of the Lie algebras of the classical groups
SU(n), SO(n), and Sp(n) are, respectively, tensor, antisymmetric, and symmetric
products of two vector spaces, and hence are matrix representations. We
consider the analogous products of three vector spaces and study when they
appear as summands in Lie algebra decompositions. The Z3-grading of the
exceptional Lie algebras provide such summands and provides representations of
classical groups on hypermatrices. The main natural application is a formal
study of three-junctions of strings and membranes. Generalizations are also
considered.Comment: 25 pages, 4 figures, presentation improved, minor correction