Representations of the modular group into the isometries of SL(3,R)/SO(3)

Joan Porti

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arXiv · 2601.15781

Representations of the modular group into the isometries of SL(3,R)/SO(3)

Joan Porti

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Abstract

We describe the topology of the variety of characters of the modular group $\mathrm{PSL}_2(\mathbb{Z})$ into the isometry group of the symmetric space $\mathrm{SL}_3(\mathbb{R})/\mathrm{SO}(3)$. This topology is determined in terms of the fixed point sets of the generators of the modular group. We also find Anosov representations on each nontrivial component.

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Joan Porti. 2026-01-22. Representations of the modular group into the isometries of SL(3,R)/SO(3). https://arxiv.org/abs/2601.15781

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