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Integrating positive energy representations of the Virasoro algebra

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arxiv 2506.08684 v1 pith:EQYHAJJR submitted 2025-06-10 math.FA math-phmath.MPmath.RT

Integrating positive energy representations of the Virasoro algebra

classification math.FA math-phmath.MPmath.RT
keywords representationvirasoroalgebraannulienergyeverypositivesemigroup
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We show that every unitary positive energy representation W of the Virasoro algebra exponentiates to a holomorphic *-representation of the semigroup of annuli by bounded operators on the Hilbert space completion of W. We use this to show that every representation of the Virasoro conformal net also carries a representation of the semigroup of annuli of the same kind.

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  1. Complex deformations of the circle: Group cohomology and Virasoro uniformization

    math-ph 2026-05 unverdicted novelty 7.0

    The paper computes the second group cohomology of complex deformations of the circle, identifies extending cocycles including a relative one with rotation number and conformal radius, and proves Virasoro uniformizatio...