  In this paper, we study the correspondence between a field theory in de
Sitter space in $D$-dimensions and a dual conformal field theory in a euclidean
space in $(D-1)$-dimensions. In particular, we investigate the form in which
this correspondence is established for a system of interacting scalar and a
vector fields propagating in de Sitter space. We analyze some necessary (but
not sufficient) conditions for which conformal symmetry is preserved in the
dual theory in $(D-1)$-dimensions, making possible the establishment of the
correspondence. The discussion that we address on this paper is framed on the
context of inflationary cosmology, so, the results obtained here pose some
relevant possibilities of application to the calculation of the fields's
correlation functions and of the primordial curvature perturbation $\zeta$, in
inflationary models including coupled scalar and vector fields.
