Representations of Involutory Subalgebras of Affine Kac–Moody Algebras

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