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

Presented by: 
P Belkale [North Carolina]
Date: 
Tuesday 28th June 2011 - 10:00 to 11:00
Venue: 
INI Seminar Room 1
Abstract: 
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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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons