Homogeneous quaternionic Kähler structures of linear type. (Q1426549)

This paper shows that a connected, simply connected and complete quaternionic Kähler manifold of dimension \(4n\geq 8\) admitting a homogeneous quaternionic Kähler structure with a special type is isometric to quaternionic hyperbolic space. The result is based on a decomposition of the space of quaternionic Kähler homogeneous structures by the irreducible representations of \(\text{Sp}(n)\text{Sp}(1)\subset \text{SO}(4n)\).