Concave Foliated Flag Structures and the SL₃(ℝ) Hitchin Component

2024/07/08 by Alexander Nolte, Nolte, Alexander, J. Maxwell Riestenberg +1
Mathematics · #20H10 #22E40 #57M50 #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · pdf · doi:10.48550/arxiv.2407.06361

openalex publication_date 2024/07/08 · openalex created_date 2024/07/11 · openalex updated_date 2026/07/28

Abstract

We give a geometric characterization of flag geometries associated to Hitchin representations in SL₃(ℝ). Our characterization is based on distinguished invariant foliations, similar to those studied by Guichard-Wienhard in PSL₄(ℝ). We connect to the dynamics of Hitchin representations by constructing refraction flows for all positive roots in general \mathfraksl_n(ℝ) in our setting. For n = 3, leaves of our one-dimensional foliations are flow-lines. One consequence is that the highest root flows are C^1+α.

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