Classification of stationary compact homogeneous special pseudo K\"ahler manifolds of semisimple groups

The variation of Hodge structure of a Calabi-Yau 3-fold induces a canonical K"ahler metric on its Kuranishi moduli space, known as the Weil-Petersson metric. Similarly, special pseudo K"ahler manifolds correspond to certain (abstract) variations of Hodge structure which generalize the above example. We give the classification of homogeneous special pseudo K"ahler manifolds of semisimple groups with compact stabilizer.