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arXiv · 2609.27125

Twisted Patterson-Sullivan densities on nilpotent covers for Anosov subgroups

Krishnendu Gongopadhyay·Neelanjan Mondal
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Abstract

Let $Γ<\mathsf{SL}(d,\mathbb R)$ be a Zariski-dense Borel-Anosov subgroup and let $φ$ be positive on its limit cone. For every $χ\in \mathrm{Hom}(Γ, \mathbb R)$, we construct twisted $(φ,χ)$-conformal densities and prove their uniqueness, atomlessness, and ergodicity. For every normal subgroup $Γ_0\lhdΓ$ with nilpotent quotient, we classify the ergodic $φ$-conformal densities of $Γ_0$ in terms of characters of $Γ/Γ_0$.

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Krishnendu Gongopadhyay, Neelanjan Mondal. 2026-09-22. Twisted Patterson-Sullivan densities on nilpotent covers for Anosov subgroups. https://arxiv.org/abs/2609.27125

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