Virtually special embeddings of integral Lorentzian lattices
Virtually special embeddings of integral Lorentzian lattices
复制标题
积分洛伦兹格子的几乎特殊嵌入
DOI：
10.1090/conm/760/15285
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Chu, Michelle
中科院分区：
文献类型：
--
作者：
Chu, Michelle
积分洛伦兹格的自同构群以等距作用在有限共体积的双曲空间上。在反射积分格的情况下，自同构群可等价于算术双曲反射群。然而，对于一个固定的维度，只有200多个反射积分洛伦兹晶格，这些只能发生在小尺寸。本文的目标是构造低维积分洛伦兹格到与直角反射群相关的幺模洛伦兹格的嵌入。作为应用，我们构造了许多离散群，它们在Haglund-Wise意义下是C-特殊的。
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 offor smallwhich are C-special in the sense of Haglund-Wise.