Low Level Representations for E10 and E11

Details Low Level Representations for E10 and E11 Low Level Representations for E10 and E11

2003-01-06

arxiv.org/abs/hep-th/0301017v2

Physics

High Energy Physics

High Energy Physics - Theory

37 pages, 2 figures, 2 tables. Contribution to the Proceedings of the Ramanujan International Symposium on Kac-Moody Algebras

Scientific paper

We work out the decomposition of the indefinite Kac Moody algebras ${E_{10}}$ and ${E_{11}}$ w.r.t. their respective subalgebras $A_9$ and $A_{10}$ at low levels. Tables of the irreducible representations with their outer multiplicities are presented for ${E_{10}}$ up to level $\ell = 18$ and for ${E_{11}}$ up to level $\ell =10$. On the way we confirm and extend existing results for ${E_{10}}$ root multiplicities, and for the first time compute non-trivial root multiplicities of ${E_{11}}$.

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