Polarization tensor in de Sitter gauge gravity

The gauge theory of the de Sitter group, SO$(1,4)$, in ambient space formalism has been considered this article. This method is essential to constructing super-conformal gravity and Quantum gravity. $10$ vector fields are needed, corresponding generators group. Using gauge-invariant Lagrangian, field equation these obtained. solutions recalled. Then, spin-$2$ potentials constructed from field. There two possibilities for presenting tensor field: rank-$2$ symmetric mixed symmetry rank-$3$ fields. To preserve conformal transformation, a must be represented by field, $\mathcal {K}_{\alpha\beta\gamma}$. rewritten using generalized polarization plane wave. calculated as combination polarization, {E}_{\alpha}$, rank-$2$, {E}_{\alpha\beta}$, which can used gravitational wave consideration. For construction tensor, arbitrary constant appear. We fix it so that, limit, $H=0$, one obtains Minkowski space-time. It shown that under some simple conditions, simultaneously transformed unitary irreducible representation groups, SO$(2,4)$.