Inhomogeneous hypercomplex structures on homogeneous manifolds

We study deformations of hypercomplex structures on compact homogeneous spaces through the complex deformation theory of the associated twister spaces. In general, we find complete parameter spaces of hypercomplex structures associated to compact semi-simple Lie groups. In particular, we discover the moduli space of hypercomplex structures on products of Hopf surfaces and on compact associated bundles of quaternionic projective spaces.