Homogeneous quaternionic Kaehler structures and quaternionic hyperbolic   space
  An explicit classification of homogeneous quaternionic Kaehler structures by real tensors is derived and we relate this to the representation-theoretic description found by Fino. We then show how the quaternionic hyperbolic space HH(n) is characterised by admitting homogeneous structures of a particularly simple type. In the process we study the properties of different homogeneous models for HH(n). 
M. Castrillon Lopez, P. M. Gadea and A. F. Swann