降级：高维中的Mazur原理
Level lowering: a Mazur principle in higher dimension
AI总结：
本文提出高维Mazur原理，通过分析Hecke代数极大理想关联的Galois表示的单值算子分拆差异，解决特征零中表示的降级问题。
摘要：
对于签名(1,d-1)的相似群的一个贫血Hecke代数$\mathbb{T}^S_ξ$的极大理想$\mathfrak m$，可以关联一个Galois $\overline{\mathbb F}_l$-表示$\overline ρ_{\mathfrak m}$以及一个Galois $\mathbb{T}_{ξ,\mathfrak m}^S$-表示$ρ_{\mathfrak m}$。对于$l\geq d$，还可以定义单值算子$\overline N_{\mathfrak m}$以及对于每个素理想$\widetilde{\mathfrak m} \subset \mathfrak m$定义$N_{\widetilde{\mathfrak m}}$，从而产生$d$的分拆$\underline{\bar d_{\mathfrak m}}$和$\underline d_{\widetilde{\mathfrak m}}$。与$GL_2$的Mazur原理一样，通过分析这些分拆之间的差异，我们推断出关于$\overline ρ_{\mathfrak m}$在特征零中的提升的信息，即所谓的降级问题。
英文摘要：
For a maximal ideal $\mathfrak m$ of some anemic Hecke algebra $\mathbb{T}^S_ξ$ of a similitude group of signature $(1,d-1)$, one can associate a Galois $\overline{\mathbb F}_l$-representation $\overline ρ_{\mathfrak m}$ as well as a Galois $\mathbb{T}_{ξ,\mathfrak m}^S$-representation $ρ_{\mathfrak m}$.For $l\geq d$, on can also define a monodromy operator $\overline N_{\mathfrak m}$ as well as $N_{\widetilde{\mathfrak m}}$ for every prime ideal $\widetilde{\mathfrak m} \subset \mathfrak m$, giving rise to partitions $\underline{\bar d_{\mathfrak m}}$ and $\underline d_{\widetilde{\mathfrak m}}$ of $d$. As with Mazur's principle for $GL_2$, analysing the difference between these partitions, we infer informations about the liftings of $\overline ρ_{\mathfrak m}$ in characteristic zero known as level lowering problem.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
