Ground-state quantum numbers of the half-filled Hubbard model

Working on a square lattice with an even number of sites N² and assuming a smooth connection between strong and weak coupling, we show that the ground state of the two-dimensional half-filled Hubbard model has momentum kₓ-ky=0, it is even under reflections, and transforms as an s wave under rotations when N/2 is even and as a d wave when N/2 is odd.