  We study the interferometric observation of intensity and polarization
anisotropies of a stochastic gravitational wave background (SGWB). We show that
the observed correlated data is defined in the group manifold of the
three-dimensional rotation. Explicit correlation between two detectors in the
interferometry experiments such as LIGO-Virgo and KAGRA is constructed in terms
of the Wigner D-functions. Our results may provide a tool for constructing data
pipelines to estimate the power spectra of the SGWB anisotropies.
