On symmetries of complex Dirac-Kaehler equation

The complex eight-component Dirac-Kaehler equation with nonzero mass is considered. It is shown that the complex Dirac-Kaehler equation is the partial case of the fermion Bhabha-type equation. It is proved that this equation is invariant relatively the algebra of pure matrix transformations as well as relatively of two different Poincare groups representations (fermion and boson ρ- representations). The complex Dirac-Kaehler equation is also described in the explicitly covariant boson form as the equation for the system of self-dual, scalar and vector fields