We show that any positive energy projective unitary representation of Diff(S^1) extends to a strongly continuous projective unitary representation of the fractional Sobolev diffeomorphisms D^s(S^1) for any real s>3, and in particular to C^k-diffeomorphisms Diff^k(S^1) with k>=4. A similar result holds for the universal covering groups provided that the representation is assumed to be a direct sum of irreducibles. As an application we show that a conformal net of von Neumann algebras on S^1 is covariant with respect to D^s(S^1), s > 3. Moreover every direct sum of irreducible representations of a conformal net is also D^s(S^1)-covariant.
Carpi, S., Del Vecchio, S., Iovieno, S., Tanimoto, Y. (2021). Positive energy representations of Sobolev diffeomorphism groups of the circle. ANALYSIS AND MATHEMATICAL PHYSICS, 11(1) [10.1007/s13324-020-00429-5].
Positive energy representations of Sobolev diffeomorphism groups of the circle
Carpi, S.;Del Vecchio, S.;Tanimoto, Y.
2021-01-01
Abstract
We show that any positive energy projective unitary representation of Diff(S^1) extends to a strongly continuous projective unitary representation of the fractional Sobolev diffeomorphisms D^s(S^1) for any real s>3, and in particular to C^k-diffeomorphisms Diff^k(S^1) with k>=4. A similar result holds for the universal covering groups provided that the representation is assumed to be a direct sum of irreducibles. As an application we show that a conformal net of von Neumann algebras on S^1 is covariant with respect to D^s(S^1), s > 3. Moreover every direct sum of irreducible representations of a conformal net is also D^s(S^1)-covariant.File | Dimensione | Formato | |
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