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Geometry and Physics: Volume IIA Festschrift in honour of Nigel Hitchin$
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Andrew Dancer, Jørgen Ellegaard Andersen, and Oscar García-Prada

Print publication date: 2018

Print ISBN-13: 9780198802020

Published to Oxford Scholarship Online: December 2018

DOI: 10.1093/oso/9780198802020.001.0001

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Wild Character Varieties, Meromorphic Hitchin Systems and Dynkin Diagrams

Wild Character Varieties, Meromorphic Hitchin Systems and Dynkin Diagrams

(p.433) 17 Wild Character Varieties, Meromorphic Hitchin Systems and Dynkin Diagrams
Geometry and Physics: Volume II

Philip Boalch

Oxford University Press

The theory of Hitchin systems is something like a ‘global theory of Lie groups’ where one works over a Riemann surface rather than just at a point. This chapter describes how one can take this analogy a few steps further by attempting to make precise the class of rich geometric objects that appear in this story (including the non-compact case) and discusses their classification, outlining a theory of ‘Dynkin diagrams’ as a step towards classifying some examples of such objects.

Keywords:   Hitchin system, non-abelian Hodge theory, quasi-Hamiltonian space, Lie group, Dynkin diagram

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