发表机构
Indian Institute of Science Education and Research (IISER) Mohali（印度科学教育研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为Anosov子群构造扭曲共形密度并证明其唯一性、无原子性和遍历性，进而利用商群特征分类幂零覆盖上正规子群的遍历共形密度。
AI 中文摘要
设$\Gamma<\mathsf{SL}(d,\mathbb R)$为Zariski稠密的Borel-Anosov子群，且$\phi$在其极限锥上为正。对每个$\chi\in \mathrm{Hom}(\Gamma, \mathbb R)$，我们构造扭曲的$(\phi,\chi)$-共形密度，并证明其唯一性、无原子性和遍历性。对每个具有幂零商的正规子群$\Gamma_0\lhd\Gamma$，我们用$\Gamma/\Gamma_0$的特征对$\Gamma_0$的遍历$\phi$-共形密度进行分类。
英文摘要
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 $Γ/Γ_0$.
CommentsPreliminary version
