%0 Journal Article %T Projective unitary representations of smooth Deligne cohomology groups %A Kiyonori Gomi %J Mathematics %D 2005 %I arXiv %X We construct projective unitary representations of the smooth Deligne cohomology group of a compact oriented Riemannian manifold of dimension 4k+1, generalizing positive energy representations of the loop group of the circle. We also classify such representations under a certain condition. The number of the equivalence classes of irreducible representations is finite, and is determined by the cohomology of the manifold. %U http://arxiv.org/abs/math/0510187v2