The involutory subalgebra $K(E_9)$ of the affine Kac–Moody algebra $E_9$ was recently shown to admit an infinite sequence of unfaithful representations of ever increasing dimensions. In this talk I will describe these representations and their associated ideals in more detail, and discuss their relevance for the issue of generalized holonomies in supergravity. From these results it emerges that the holonomy groups so far discussed in the literature are mere shadows (in a Platonic sense) of a much larger structure.