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#### On spinorial representations of involutory subalgebras of Kac-Moody algebras

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##### Fulltext (public)

1811.11659.pdf

(Preprint), 386KB

##### Supplementary Material (public)

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##### Citation

Kleinschmidt, A., Nicolai, H., & Vigano, A. (in preparation). On spinorial representations of involutory subalgebras of Kac-Moody algebras.

Cite as: http://hdl.handle.net/21.11116/0000-0002-AF5C-3

##### Abstract

The representation theory of involutory (or 'maximal compact') subalgebras of
infinite-dimensional Kac-Moody algebras is largely terra incognita, especially
with regard to fermionic (double-valued) representations. Nevertheless, certain
distinguished such representations feature prominently in proposals of possible
symmetries underlying M theory, both at the classical and the quantum level.
Here we summarise recent efforts to study spinorial representations
systematically, most notably for the case of the hyperbolic Kac-Moody algebra
$E_{10}$ where spinors of the involutory subalgebra $K(E_{10})$ are expected to
play a role in describing algebraically the fermionic sector of $D=11$
supergravity and M theory. Although these results remain very incomplete, they
also point towards the beginning of a possible explanation of the fermion
structure observed in the Standard Model of Particle Physics.