  Understanding the interplay between the topological nature and the symmetry
property of interacting systems has been a central matter of condensed matter
physics in recent years. In this Letter, we establish nonperturbative
constraints on the quantized Hall conductance of many-body systems with
arbitrary interactions. Our results allow one to readily determine the
many-body Chern number modulo a certain integer without performing any
integrations, solely based on the rotation eigenvalues and the average particle
density of the many-body ground state.
