Hypermatrix factors for string and membrane junctions
High Energy Physics - Theory
2010-12-09 v2 Mathematical Physics
Combinatorics
math.MP
Representation Theory
Abstract
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.
Cite
@article{arxiv.1001.5166,
title = {Hypermatrix factors for string and membrane junctions},
author = {Yuhan Fang and Shir Levkowitz and Hisham Sati and Daniel Thompson},
journal= {arXiv preprint arXiv:1001.5166},
year = {2010}
}
Comments
25 pages, 4 figures, presentation improved, minor corrections