We define a level for a large class of Lorentzian Kac-Moody algebras. Using this we find the representation content of very extended $A_{ D-3}$ and $E_8$ (i.e. $E_{ 11}$) at low levels in terms of $A_{ D-1}$ and $A_{ 10}$ representations respectively. The results are consistent with the conjectured very extended $A_8$ and $E_{ 11}$ symmetries of gravity and maximal supergravity theories given respectively in hep-th/0104081 and hep-th/0107209. We explain how these results provided further evidence for these conjectures.
Categories: hep-th