Higher order M theory corrections and the Kac-Moody algebra E10
  It has been conjectured that the classical dynamics of M theory is equivalent to a null geodesic motion in the infinite-dimensional coset space E10/K(E10) where K(E10) is the maximal compact subgroup of the hyperbolic Kac-Moody group E10. We here provide further evidence for this conjecture by showing that the leading higher order corrections, quartic in the curvature and related three-form dependent terms, correspond to negative imaginary roots of E10. The conjecture entails certain predictions for which higher order corrections are allowed: in particular corrections of type R^M (DF)^N are compatible with E10 only for M+N=3k+1. Furthermore, the leading parts of the R^4, R^7,... terms are predicted to be associated with singlets under the SL(10) decomposition of E10. Although singlets are extremely rare among the altogether 4,400,752,653 representations of SL(10) appearing in E10 up to level l \leq 28, there are indeed singlets at levels l=10 and l =20 which do match with the R^4 and the expected R^7 corrections. Our analysis indicates a far more complicated behavior of the theory near the cosmological singularity than suggested by the standard homogeneous ans\"atze. 
T. Damour and H. Nicolai