Extended E8 invariance of 11-dimensional supergravity

The hyperbolic Kac-Moody algebra E-10 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 E-10/K(E-10). 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 E-8/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.