Gauging the Heisenberg algebra of special quaternionic manifolds

We show that in N=2 supergravity, with a special quaternionic manifold of (quaternionic) dimension h1+1 and in the presence of h2 vector multiplets, a (h2+1)-dimensional Abelian algebra, intersecting the (2h1+3)-dimensional Heisenberg algebra of quaternionic isometries, can be gauged provided the h2+1 symplectic charge-vectors VI, have vanishing symplectic invariant scalar product VI×VJ=0. For compactifications on Calabi-Yau three-folds with Hodge numbers (h1,h2) such condition generalizes the half-flatness condition as used in the recent literature. We also discuss non-Abelian extensions of the above gaugings and their consistency conditions.