  We provide a full quantization of the vacuum Gowdy model with local
rotational symmetry. We consider a redefinition of the constraints where the
Hamiltonian Poisson-commutes with itself. We then apply the canonical
quantization program of loop quantum gravity within an improved dynamics
scheme. We identify the exact solutions of the constraints and the physical
observables, and we construct the physical Hilbert space. It is remarkable that
quantum spacetimes are free of singularities. New quantum observables naturally
arising in the treatment partially codify the discretization of the geometry.
The preliminary analysis of the asymptotic future/past of the evolution
indicates that the existing Abelianization technique needs further refinement.
