Classification of quaternionic skew-Hermitian symmetric spaces

We provide a complete classification of quaternionic skew-Hermitian symmetric spaces, namely symmetric spaces that admit a torsion-free ${\mathrm{S}\mathrm{O}}^{\ast }(2n)\mathrm{S}\mathrm{p}(1)$-structure for arbitrary $n>1$. Moreover, we prove that any homogeneous quaternionic skew-Hermitian manifold is necessarily a symmetric space.