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In this paper, we study the correspondence between a field theory in deSitter space in $D$-dimensions and a dual conformal field theory in a euclideanspace in $(D-1)$-dimensions. In particular, we investigate the form in whichthis correspondence is established for a system of interacting scalar and avector fields propagating in de Sitter space. We analyze some necessary (butnot sufficient) conditions for which conformal symmetry is preserved in thedual theory in $(D-1)$-dimensions, making possible the establishment of thecorrespondence. The discussion that we address on this paper is framed on thecontext of inflationary cosmology, so, the results obtained here pose somerelevant possibilities of application to the calculation of the fields'scorrelation functions and of the primordial curvature perturbation $\zeta$, ininflationary models including coupled scalar and vector fields.

de Sitter symmetries and inflationary scalar-vector models