We show that pseudo-Riemannian almost quaternionic homogeneous spaces with index 4 and an H-irreducible isotropy group are locally isometric to a pseudo-Riemannian quaternionic Kähler symmetric space if the dimension is at least 16. In dimension 12 we give a non-symmetric example.
We show that pseudo-Riemannian almost quaternionic homogeneousspaces with index4 and anH-irreducible isotropy group are locally isometric to a pseudo-Riemannianquaternionic K ̈ahler symmetric space if the dimension is at least 16. In dimension 12we give a non-symmetric example.Keywords: Homogeneous spaces, symmetric spaces, pseudo-Riemannian manifolds,almost quaternionic structuresMSC classification: 53C26, 53C30, 53C35, 53C50