  Using symmetries of the current correlation function, we analyze the
frequency dependence of the photon energy absorption rate of a striped Hall
gas. Since the magnetic translational symmetry is spontaneously broken in the
striped Hall gas, a Nambu-Goldstone (NG) mode appears. It is shown that the NG
mode causes a sharp absorption at the zero energy in the long wavelength limit
by using the single mode approximation. The photon energy absorption rate at
the NG mode frequency strongly depends on the direction of the wave number
vector. Whereas, the absorption rate at the cyclotron frequency does not depend
on the direction of the wave number vector in the long wavelength limit. The
cyclotron resonance is not affected in the striped Hall gas. Our result
supplements the Kohn's theorem in the system of the NG mode.
