Projective unitary representations of smooth Deligne cohomology groups
The purpose of this paper is to construct and classify admissible representations of the smooth Deligne cohomology group. The author constructs 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 at level 2. For the construction and the classification of admissible representations the author studies the structure of this cohomology group and its central extension, using a short exact sequence which this group fits into. So, the study of the structure also allows to generalize some properties of positive energy representations of loop groups. The author classifies such representations under a certain condition. The number of equivalence classes of irreducible representations is finite and is determined by the cohomology of the manifold. Finally, in the Appendix, some general properties of unitary representations on Hilbert spaces are proved. A kind of Schur's lemma plays an important role in the classification.
infinite-dimensional representation p-form gauge theory
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