Reversible linear differential equations

2008/05/30 by Sanabria, Camilo
#14F05 #34M15 #Algebraic Geometry (math.AG) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.0805.4649

Abstract

Let ∇ be a meromorphic connection on a vector bundle over a compact Riemann surface Γ. An automorphism σ:Γ→Γ is called a symmetry of ∇ if the pull-back bundle and the pull-back connection can be identified with ∇. We study the symmetries by means of what we call the Fano Group; and, under the hypothesis that ∇ has a unimodular reductive Galois group, we relate the differential Galois group, the Fano group and the symmetries by means of an exact sequence.

Related

• On linear differential equations with reductive Galois group
• Differential Galois groups of G-connections with Coxeter singularities
• Folded and contracted solutions of coupled classical dynamical\n Yang-Baxter and reflection equations
• Fano versus Calabi - Yau
• Spectra and strains