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arXiv · 1811.11659

On spinorial representations of involutory subalgebras of Kac-Moody algebras

Axel Kleinschmidt·Hermann Nicolai·Adriano Viganò
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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.

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Axel Kleinschmidt, Hermann Nicolai, Adriano Viganò. 2018-11-28. On spinorial representations of involutory subalgebras of Kac-Moody algebras. https://arxiv.org/abs/1811.11659

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