We fix an infinite field k of any characteristic. In this paper we consider the following three prehomogeneous vector spaces (1) G=GL(2)k1xGL(2)k where k1/k is a fixed quadratic extension and V is the space of pairs of binary Hermitian forms, (2) G=GL(1)kXGL(2)k1 where k1/k is a fixed cubic extension and V is an eight dimensional representation of G which becomes the D4 case in [7] after a suitable field extension of k, (3) G=GL(3) k1XGL(2)k where k1/k is a fixed quadratic extension and V is the space of pairs of ternary Hermitian forms.
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