Quantum pumping in the magnetic field: Role of discrete symmetries

We consider an effect of the discrete spatial symmetries and magnetic field on the adiabatic charge pumping in mesoscopic systems. In the general case, there is no symmetry of the pumped charge with respect to the inversion of magnetic field Q(B)≠Q(-B). We find that the reflection symmetries give rise to relations Q(B)=Q(-B) or Q(B)=-Q(-B) depending on the orientation of the reflection axis. In the presence of the center of inversion Q(B)≡0. Additional symmetries may arise in the case of bilinear pumping.