2024/11/13 by Irfan Habib, Habib, Irfan · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Elasticity and Wave Propagation #FOS: Mathematics #Nonlinear Photonic Systems #Numerical methods for differential equations #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2411.08749
openalex publication_date 2024/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
Any maximal root subsystem of a finite crystallographic reduced root system is either a closed root subsystem or its dual is a closed root subsystem in the dual root system. In this article, we classify the maximal root subsystems of an affine reflection system (reduced and non-reduced) and prove that this result holds in much more generality for reduced affine reflection systems. Moreover, we explicitly determine when a maximal root subsystem is a maximal closed root subsystem. Using our classification, at the end, we characterize the maximal root systems of affine reflection systems with nullity less than or equal to 2 using Hermite normal forms; especially for Saito's EARS of nullity 2. This in turn classifies the maximal subgroups of the Weyl group of an affine reflection system that are generated by reflections.