  The hyperbolic Kac-Moody algebra E10 has repeatedly been suggested to play a
crucial role in the symmetry structure of M-theory. Recently, following the
analysis of the asymptotic behaviour of the supergravity fields near a
cosmological singularity, this question has received a new impulse. It has been
argued that one way to exhibit the symmetry was to rewrite the supergravity
equations as the equations of motion of the non-linear sigma model E10/K(E10).
This attempt, in line with the established result that the scalar fields which
appear in the toroidal compactification down to three spacetime dimensions form
the coset E8/SO(16), was verified for the first bosonic levels in a level
expansion of the theory. We show that the same features remain valid when one
includes the gravitino field
