2010/03/10 by Eduard Looijenga, Looijenga, Eduard
Mathematics · Physics and Astronomy · #14D07 (Secondary) #32G34 (Primary) #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum Algebra (math.QA) #Quantum chaos and dynamical systems #Representation Theory (math.RT) #math.AG #math.QA #math.RT #msc:14D07 #msc:32G34
paper · pdf · doi:10.48550/arxiv.1003.2033
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
openalex publication_date 2010/03/10 · arxiv created 2011/01/11 · arxiv updated 2011/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.