Bethe Subspaces and Toric Arrangements
Published:Dec 29, 2025 14:02
•1 min read
•ArXiv
Analysis
This paper explores the geometry of Bethe subspaces, which are related to integrable systems and Yangians, and their connection to toric arrangements. It provides a compactification of the parameter space for these subspaces and establishes a link to the logarithmic tangent bundle of a specific geometric object. The work extends and refines existing results in the field, particularly for classical root systems, and offers conjectures for future research directions.
Key Takeaways
- •Introduces and studies Bethe subspaces within the context of trigonometric holonomy Lie algebras.
- •Provides a compactification of the parameter space for Bethe subspaces using the minimal wonderful model of a toric arrangement.
- •Establishes connections between Bethe subspaces and the logarithmic tangent bundle.
- •Refines existing results and offers conjectures for future research, particularly in the context of Yangians and quantum cohomology.
Reference
“The paper proves that the family of Bethe subspaces extends regularly to the minimal wonderful model of the toric arrangement.”