Homogeneous Quaternionic Kahler Structures and Quaternionic Hyperbolic Space

Abstract

An explicit classification of homogeneous quaternionic Kahler 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 \({\mathbb H}H(n)\) is characterised by admitting homogeneous structures of a particularly simple type. In the process we study the properties of different homogeneous models for \({\mathbb H}H(n).\)