A topological interpretation of the KZ system
Quantum Algebra
2011-01-12 v6 Algebraic Geometry
Representation Theory
Abstract
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.
Keywords
Cite
@article{arxiv.1003.2033,
title = {A topological interpretation of the KZ system},
author = {Eduard Looijenga},
journal= {arXiv preprint arXiv:1003.2033},
year = {2011}
}
Comments
The main result has been strengthened (Thm 3.7) and some of the discussion has been expanded. To appear in the Proceedings of the Second MSJ Seasonal Institute 2009 on Arrangements of Hyperplanes