Strongly degenerate homogeneous pseudo-K\"ahler structures of linear type and complex plane waves

We study the class ${\mathcal{K}}_2+{\mathcal{K}}_4$ of homogeneous pseudo-K"ahler structures in the strongly degenerate case. The local form and the holonomy of a pseudo-K"ahler manifold admitting such a structure is obtained, leading to a possible complex generalization of homogeneous plane waves. The same question is tackled in the case of pseudo-hyper-K"ahler and pseudo-quaternion K"ahler manifolds.