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Geometric unitarity of the KZ/Hitchin connection on conformal blocks in genus 0

Geometric unitarity of the KZ/Hitchin connection on conformal blocks in genus 0

Update: 2011-06-29
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We prove that the vector bundles of conformal blocks, on moduli spaces of genus zero curves with marked points, for arbitrary simple Lie algebras and arbitrary integral levels, carry geometrically defined unitary metrics (as conjectured by K. Gawedzki) which are preserved by the Knizhnik-Zamolodchikov/Hitchin connection. Our proof builds upon the work of T. R. Ramadas who proved this unitarity statement in the case of the Lie algebra sl(2) (and genus zero) and arbitrary integral level.
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Geometric unitarity of the KZ/Hitchin connection on conformal blocks in genus 0

Geometric unitarity of the KZ/Hitchin connection on conformal blocks in genus 0

Cambridge University