Work

Hyperplane arrangements and Vinberg's θ-groups

Year: 2026

Type: article

Abstract: Let g = ⨁ i ∈ Z / m Z g i be a periodically graded semisimple complex Lie algebra. In this note, we give a uniform proof of the recent result by W. de Graaf and H. V. Lê that the hyperplane arrangement determined by the restrictions of the roots of g to a Cartan subspace c ⊂ g 1 coincides with the hyperplane arrangement of (complex) reflections of the little Weyl group of g = ⨁ i ∈ Z / m Z g i .

Source: Journal of Algebra

DOI: 10.1016/j.jalgebra.2025.12.023

Authors: Filippo Ambrosio, Andrea Santi

Institutions: Friedrich Schiller University Jena, University of Rome Tor Vergata

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,310