The IIA, IIB and eleven-dimensional theories and their common E11 origin

We show that the commonly considered half BPS solutions of eleven-dimensional supergravity and the ten-dimensional type II theories, when expressed in terms of E11 group elements, take the universal form exp(-((1)/(2))lnNβ·H)exp((1-N)Eβ). Using this formula we find new potential solutions to the E11 non-linearly realisations corresponding to active fields which are beyond those in the supergravity approximations. These include the space filling nine brane of the IIB theory. We use E11 to give a correspondence between the fields of the eleven-dimensional and the IIA and IIB non-linear realisations without assuming any dimensional reduction. As one consequence, we find the eleven-dimensional origin of the eight brane solution of the massive IIA theory