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Abstract

We consider the subalgebras of split real, non-twisted affine Kac-Moody Lie
algebras that are fixed by the Chevalley involution. These infinite-dimensional
Lie algebras are not of Kac-Moody type and admit finite-dimensional unfaithful
representations. We exhibit a formulation of these algebras in terms of
$\mathbb{N}$-graded Lie algebras that allows the construction of a large class
of representations using the techniques of induced representations. We study
how these representations relate to previously established spinor
representations as they arise in the theory of supergravity.