Characteristic classes of parabolic foliations of the series B, C, and D, and the degrees of isotropic Grassmanians (Q1819418)

The author examines the characteristic homomorphism of locally homogeneous foliations obtained from cosets of a maximal parabolic subgroup in a semisimple Lie group G, which is assumed to belong to one of the classical series B, C, D (the A-series case has been described in one of the author's earlier papers). In each case a certain explicit subspace of \(H^*(W_ N)\) is given which is complementary to the kernel of the characteristic homomorphism. As a partial result, degrees of all the considered isotropic Grassmanians are listed.