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VOL. 62 | 2012 The KZ system via polydifferentials


We show that the KZ system has a topological interpretation in the sense that it may be understood as a variation of complex mixed Hodge structure whose successive pure weight quotients are polarized. This in a sense completes and elucidates work of Schechtman–Varchenko done in the early 1990's. A central ingredient is a new realization of the irreducible highest weight representations of a Lie algebra of Kac–Moody type, namely on an algebra of rational polydifferentials on a countable product of Riemann spheres. We also obtain the kind of properties that in the $\mathfrak{sl} (2)$ case are due to Ramadas and are then known to imply the unitarity of the WZW system in genus zero.


Published: 1 January 2012
First available in Project Euclid: 24 November 2018

zbMATH: 1260.32004
MathSciNet: MR2933798

Digital Object Identifier: 10.2969/aspm/06210189

Primary: 32G34
Secondary: 14D07

Keywords: highest weight module , KZ system , polydifferentials

Rights: Copyright © 2012 Mathematical Society of Japan


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