  In this article we analyze the quotients of the maximal compact subalgebras
of the split real Kac-Moody algebras of the En series resulting from the
generalized spin representations introduced in part 1. It turns out that these
quotients satisfy a Cartan-Bott periodicity.
  Our findings are also meaningful in the finite-dimensional cases of A2 + A1,
A4, D5, E6, E7, E8, where it turns out that the generalized spin representation
is injective. Consequently the observed Cartan-Bott periodicity provides a
structural explanation for the seemingly sporadic isomorphism types of the
maximal compact Lie subalgebras of the split real Lie algebras of types E6, E7,
E8.
