论文标题
几乎是整体洛伦兹晶格的特殊嵌入
Virtually special embeddings of integral Lorentzian lattices
论文作者
论文摘要
洛伦兹晶格整体晶格的自动形态群在具有有限的covolume的双曲线空间上作用。在反射性积分晶格的情况下，自动态组可与算术双曲反射组相称。但是，对于固定尺寸，只有许多反射性积分洛伦兹晶格有限，而这些晶格只能出现在小维度上。该注释的目的是将低维整体洛伦兹晶格的嵌入到与右角反射基团相关的单模型的洛伦兹晶格中。作为一个应用程序，我们构造了许多$ \ mathrm {isom}的离散组（\ m athbb {h}^n）$，用于小$ n $，在haglund的意义上是c特定的。
The automorphism groups of integral Lorentzian lattices act by isometries on hyperbolic space with finite covolume. In the case of reflective integral lattices, the automorphism groups are commensurable to arithmetic hyperbolic reflection groups. However, for a fixed dimension, there is only finitely many reflective integral Lorentzian lattices, and these can only occur in small dimensions. The goal of this note is to construct embeddings of low-dimensional integral Lorentzian lattices into unimodular Lorentzian lattices associated to right-angled reflection groups. As an application, we construct many discrete groups of $\mathrm{Isom}(\mathbb{H}^n)$ for small $n$ which are C-special in the sense of Haglund-Wise.
