Entropy Rigidity for Maximal Representations
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908750987657216 |
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| author | Yao, Zhufeng |
| author_facet | Yao, Zhufeng |
| contents | Let $Γ\subset \mathsf{PSL}(2,\mathbb{R})$ be a lattice and $ρ:Γ\to \mathsf{Sp}(2n,\mathbb{R})$ be a maximal representation. We show that $ρ$ satisfies a measurable $(1,1,2)-$hypertransversality condition. With this we define a measurable Gromov product and the Bowen-Margulis-Sullivan measure associated to the unstable Jacobian introduced by Pozzetti, Sambarino and Wienhard. As a main application, we prove a strong entropy rigidity result for $ρ$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_03585 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Entropy Rigidity for Maximal Representations Yao, Zhufeng Differential Geometry Dynamical Systems 22E40 Let $Γ\subset \mathsf{PSL}(2,\mathbb{R})$ be a lattice and $ρ:Γ\to \mathsf{Sp}(2n,\mathbb{R})$ be a maximal representation. We show that $ρ$ satisfies a measurable $(1,1,2)-$hypertransversality condition. With this we define a measurable Gromov product and the Bowen-Margulis-Sullivan measure associated to the unstable Jacobian introduced by Pozzetti, Sambarino and Wienhard. As a main application, we prove a strong entropy rigidity result for $ρ$. |
| title | Entropy Rigidity for Maximal Representations |
| topic | Differential Geometry Dynamical Systems 22E40 |
| url | https://arxiv.org/abs/2601.03585 |