Bounded diagonal orbits in homogeneous spaces over function fields

2025/04/24 by Huang, Qianlin, Shi, Ronggang
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.17644

Abstract

This paper is about topological rigidity of diagonal group actions on the homogeneous \SL₄(\F( (t^-1) ))/\SL₄(\F[t]) where \F is a finite field of characteristic 3. We show that there is a non-closed relatively compact orbit of the diagonal group.

Citations

• On the t-adic Littlewood Conjecture
• Diagonal actions in positive characteristic
• Invariant measures and the set of exceptions to Littlewood's conjecture
• Metric Diophantine approximation over a local field of positive characteristic
• Strong Approximation for Semi-Simple Groups Over Function Fields
• Algebraic Number Theory

Related

• A non-homogeneous orbit of a diagonal subgroup
• Closed orbits for the diagonal group and well-rounded lattices
• Homogeneous orbit closures and applications
• Diagonal orbits in the wonderful compactification
• Simultaneously bounded and dense orbits for commuting Cartan actions