Irreducible representations of E theory

Abstract

We construct the [Formula: see text] theory analogue of the particles that transform under the Poincaré group, that is, the irreducible representations of the semi-direct product of the Cartan involution subalgebra of [Formula: see text] with its vector representation. We show that one such irreducible representation has only the degrees of freedom of 11-dimensional supergravity. This representation is most easily discussed in the light cone formalism and we show that the duality relations found in [Formula: see text] theory take a particularly simple form in this formalism. We explain that the mysterious symmetries found recently in the light cone formulation of maximal supergravity theories are part of [Formula: see text]. We also argue that our familiar space–times have to be extended by additional coordinates when considering extended objects such as branes.