Low Level Representations for E10 and E11

Nicolai, Hermann; Fischbacher, Thomas

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Low Level Representations for E10 and E11

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Nicolai, Hermann
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

Fischbacher, Thomas
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Nicolai, H., & Fischbacher, T. (2004). Low Level Representations for E10 and E11. In N. Sthanumoorthy, & K. C. Misra (Eds.), Proceedings of International Symposium on Kac Moody Algebras and Applications (pp. 191-228). Providence, RI: American Mathematical Society.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-5090-C

Abstract

We work out the decomposition of the indefinite Kac Moody algebras E10 and E11 w.r.t. their respective subalgebras A9 and A10 at low levels. Tables of the irreducible representations with their outer multiplicities are presented for E10 up to level ` = 18 and for E11 up to level ` = 10. On the way we confirm and extend existing results for E10 root multiplicities, and for the first time compute non-trivial root multiplicities of E11.