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In this paper we continue to study a class of four-dimensional gravity modelswith n Abelian vector fields and Sp(2n)/U(n) coset of scalar fields. This classcontains General Relativity (n=0) and Einstein-Maxwell dilaton-axion theory(n=1), which arizes in the low-energy limit of heterotic string theory. Weperform reduction of the model with arbitrary $n$ to three dimensions and studythe subgroup of non-gauge symmetries of the resulting theory. First, we find anexplicit form these symmetries using Ernst matrix potential formulation.Second, we construct new matrix variable which linearly transforms under theaction of the non-gauge transformations. Finally, we establish one generalinvariant of the non-gauge symmetry subgroup, which allow us to clarify thissubgroup structure.Comment: 12 pages in LaTe

Letter: Charging Symmetries and Linearizing Potentials for Gravity Models with Symplectic Symmetry