Very extended E8 and A8 at low levels, gravity and supergravity

Abstract

We define a level for a large class of Lorentzian Kac–Moody algebras. Using this we find the representation content of very extended AD−3 and E8 (i.e., E11) at low levels in terms of AD−1 and A10 representations, respectively. The results are consistent with the conjectured very extended A8 and E11 symmetries of gravity and maximal supergravity theories given respectively in preprints hep-th/0104081 and hep-th/0107209. We explain how these results provided further evidence for these conjectures.