A topological interpretation of the KZ system

Details A topological interpretation of the KZ system A topological interpretation of the KZ system

2010-03-10

arxiv.org/abs/1003.2033v6

Mathematics

Quantum Algebra

The main result has been strengthened (Thm 3.7) and some of the discussion has been expanded. To appear in the Proceedings of

Scientific paper

We show that the KZ system has a purely 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.

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