Parabolic and equal-rank subroot systems with applications to symmetric spaces and flag manifolds

Abstract

Using the algebraic structure of subroot systems in the root system of a complex simple Lie algebra g, we prove a generalization for compact homogeneous spaces with positive Euler characteristic of the 'strange formula' of Freudenthal and de-Vries. We also derive formulae for the Chern classes of flag manifolds and the defect of the corresponding dual or discriminant varieties.