  We discuss the polarizational study of isotropic gravitational wave
backgrounds with the second generation detector network, paying special
attention to the impacts of adding LIGO-India. The backgrounds can be
characterized by at most five spectral components (three parity-even ones and
two parity-odd ones). They can be algebraically decomposed through the
difference of the corresponding overlap reduction functions defined for the
individual spectra. We newly identify two interesting relations between the
overlap reduction functions, and these relations generally hamper the algebraic
decomposition in the low frequency regime $f \lesssim 30$Hz. We also find that
LIGO-India can significantly improve the network sensitives to the odd spectral
components.

Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology