Unitarity of the KZ/Hitchin connection on conformal blocks in genus 0 for arbitrary Lie algebras
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Publication:456613
DOI10.1016/J.MATPUR.2012.02.008zbMATH Open1277.14035arXiv1101.5846OpenAlexW2046023755WikidataQ60326247 ScholiaQ60326247MaRDI QIDQ456613
Author name not available (Why is that?)
Publication date: 16 October 2012
Published in: (Search for Journal in Brave)
Abstract: We prove that the vector bundles of conformal blocks, on suitable moduli spaces of genus zero curves with marked points, for arbitrary simple Lie algebras and arbitrary integral levels, carry unitary metrics of geometric origin which are preserved by the Knizhnik-Zamolodchikov/Hitchin connection (as conjectured by Gawedzki). Our proof builds upon the work of Ramadas who proved this unitarity statement in the case of the Lie algebra sl(2) (and genus 0). We note that unitarity has been proved in all genera (including genus 0) by the combined work of Kirillov and Wenzl in the 90's (their approach does not yield a concrete metric).
Full work available at URL: https://arxiv.org/abs/1101.5846
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