تقرير
Concave Foliated Flag Structures and the $\text{SL}_3(\mathbb{R})$ Hitchin Component
| العنوان: | Concave Foliated Flag Structures and the $\text{SL}_3(\mathbb{R})$ Hitchin Component |
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| المؤلفون: | Nolte, Alexander, Riestenberg, J. Maxwell |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Geometric Topology, Mathematics - Differential Geometry, 57M50, 20H10, 22E40 |
| الوصف: | We give a geometric characterization of flag geometries associated to Hitchin representations in $\text{SL}_3(\mathbb{R})$. Our characterization is based on distinguished invariant foliations, similar to those studied by Guichard-Wienhard in $\text{PSL}_4(\mathbb{R})$. We connect to the dynamics of Hitchin representations by constructing refraction flows for all positive roots in general $\mathfrak{sl}_n(\mathbb{R})$ in our setting. For $n = 3$, leaves of our one-dimensional foliations are flow-lines. One consequence is that the highest root flows are $C^{1+\alpha}$. Comment: 43 pages, 7 figures. Comments welcome! |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.06361 |
| رقم الأكسشن: | edsarx.2407.06361 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |