On Invariant Hypercomplex Structures on Homogeneous Spaces

An existence of invariant hypercomplex structure on compact homogeneous spaces implies strong restrictions on their root structure and consequently on their characteristic Pontrjagin classes and the corresponding Chern classes. We describe these constraints by making use of Lie theory. 2010 Mathematics Subject Classification. Primary: 22F30, 32Q60, Secondary: 22E60, 57R20.