Low Level Representations for E10 and E11

Abstract

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 $E_{11}$.

37 pages, 2 figures, 2 tables. Contribution to the Proceedings of the Ramanujan International Symposium on Kac-Moody Algebras and Applications, ISKMAA-2002, Jan. 28--31, Chennai,India. Version to be published in Contemporary Mathematics, minor corrections. Source version now contains also A2 level decomposition for Feingold-Frenkel algebra AE3 up to level 56, in addition to tables for E10 and E11 that contain more data than presented in the text

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