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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

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

Philip Boalch

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198802020.003.0017

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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