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

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1811.11659.pdf

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##### Citation

Kleinschmidt, A., Nicolai, H., & Vigano, A. (2020). On spinorial representations
of involutory subalgebras of Kac-Moody algebras. In *Partition Functions and Automorphic Forms*
(pp. 179-215). Springer.

Cite as: https://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.

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.