Simple variables for AdS5×S5AdS5×S5 superspace

We introduce simple variables for describing the AdS5×S5AdS5×S5 superspace, i.e.  PSU(2,2|4)SO(4,1)×SO(5). The idea is to embed the coset superspace into a space described by variables which are in linear (ray) representations of the supergroup PSU(2,2|4)PSU(2,2|4) by imposing certain supersymmetric quadratic constraints (up to two overall U(1) factors). The construction can be considered as a supersymmetric generalisation of the elementary realisations of the AdS5AdS5 and the S5S5 spaces by the SO(4,2) and SO(6) invariant quadratic constraints on two six-dimensional flat spaces.