Light-cone superstring in AdS space-time

We consider fixing the bosonic light-cone gauge for string in AdS space in the phase space framework, i.e., by choosing x+=τ, and by choosing σ so that P+ is distributed uniformly (its density P+ is independent of σ). We discuss classical bosonic string in AdSd and superstring in AdS5xS5. In the latter case the starting point is the action found in hep-th/0007036, where the κ-symmetry is fixed by a fermionic light-cone type gauge. We derive the light-cone Hamiltonian in the AdS5xS5 case and in the case of superstring in AdS3xS3. We also obtain a realization of the generators of the basic superalgebra psu(2,2 vertical bar 4) in terms of AdS5xS5 superstring coordinate 2-d fields in the light-cone gauge