Hitchin systems on hyperelliptic curves
P.I. Borisova, O.K. Sheinman
TL;DR
This paper studies hyperelliptic Hitchin systems, providing explicit formulas for Darboux coordinates on spectral curves, especially focusing on rank 2 gauge groups on genus 2 curves, advancing understanding of integrable systems.
Contribution
It introduces explicit formulas for Darboux coordinates in hyperelliptic Hitchin systems for classical Lie groups, with detailed analysis for rank 2 on genus 2 curves.
Findings
Explicit formulas for Darboux coordinates on spectral curves
Detailed analysis of rank 2 gauge groups on genus 2 curves
Advancement in understanding hyperelliptic Hitchin systems
Abstract
We describe a class of spectral curves and find explicit formulas for Darboux coordinates for hyperelliptic Hitchin systems corresponding to classical simple Lie groups. We consider in detail the systems with classical rank 2 gauge groups on genus 2 curves.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsNonlinear Waves and Solitons · Black Holes and Theoretical Physics · Advanced Algebra and Geometry