  We review the recently constructed non-trivial fermionic representations of
the infinite-dimensional subalgebra K(E10) of the hyperbolic Kac--Moody algebra
E10. These representations are all unfaithful (and more specifically, of finite
dimension). In addition we present their decompositions under the various
finite-dimensional subgroups associated with some maximal supergravities in
dimensions D<=11, and the projectors for `spin-7/2' which have not been given
before. Those representations that have not been derived from supergravity
still have to find a role and a proper physical interpretation in the
conjectured correspondence between E10 and M-theory. Nevertheless, they provide
novel mathematical structures that could shed some light on fundamental
questions in supergravity and on the possible role of K(E10) as an `R-symmetry'
of M-theory, and perhaps also on the algebra E10 itself.
