An E11 invariant gauge fixing

We consider the non-linear realisation of the semi-direct product of E11 and its vector representation which leads to a spacetime with tangent group that is the Cartan involution invariant subalgera of E11. We give an alternative derivation of the invariant tangent space metric that this space-time possesses and compute this metric at low levels in eleven, five and four dimensions. We show that one can gauge fix the non-linear realisation in an E11 invariant manner.