  Tensor and matrix formulations of Dirac-K\"ahler equation for massive and
massless fields are considered. The equation matrices obtained are simple
linear combinations of matrix elements in the 16-dimensional space. The
projection matrix-dyads defining all the 16 independent equation solutions are
found. A method of computing the traces of 16-dimensional Petiau-Duffin-Kemmer
matrix product is considered. It is shown that the symmetry group of the
Dirac-K\"ahler tensor fields is SO(4,2). The conservation currents
corresponding this symmetry are constructed. Supersymmetry of the
Dirac-K\"ahler fields with tensor and spinor parameters is analyzed. We show
the possibility of constructing a gauge model of interacting Dirac-K\"ahler
fields where the gauge group is the noncompact group under consideration.
