Wild character varieties, meromorphic Hitchin systems and Dynkin diagrams
Algebraic Geometry
2017-09-26 v4 Differential Geometry
Representation Theory
Exactly Solvable and Integrable Systems
Abstract
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. We'll describe 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 discuss their classification, outlining a theory of "Dynkin diagrams" as a step towards classifying some examples of such objects.
Keywords
Cite
@article{arxiv.1703.10376,
title = {Wild character varieties, meromorphic Hitchin systems and Dynkin diagrams},
author = {Philip Boalch},
journal= {arXiv preprint arXiv:1703.10376},
year = {2017}
}
Comments
21 pages, to appear in Hitchin's 70th birthday proceedings. v3: more on parahoric bundles, v4: minor improvements/clarifications