Projective unitary representations of smooth Deligne cohomology groups
type: Item
instance of: scholarly article
title: Projective unitary representations of smooth Deligne cohomology groups
zbMATH Open document ID: 1179.53044
author: Kiyonori Gomi
published in: Journal of Geometry and Physics
publication date: 2009-08-26T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0510187
review text: 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.
reviewed by: Corina Mohorianu
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C08
Mathematics Subject Classification ID: 22A25
Mathematics Subject Classification ID: 14F43
Mathematics Subject Classification ID: 22E65
Mathematics Subject Classification ID: 58B25
zbMATH DE Number: 5598306
zbMATH Keywords: smooth Deligne cohomology
zbMATH Keywords: infinite-dimensional representation p-form gauge theory
zbMATH Keywords: gerbe
MaRDI profile type: Publication
OpenAlex ID: W2025390203
arXiv ID: math/0510187
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DOI: 10.1016/J.GEOMPHYS.2009.06.012
description: scientific article