Lorentzian Coxeter系统的极限方向
Limit Directions for Lorentzian Coxeter Systems
摘要：
每一个考克斯特群都有一个几何表示，它是由实向量空间中的反射生成的群。在射影表示空间中，极限方向是内射序列在某个基点轨道上的极限。极限根是可以从单根开始得到的极限方向。本文研究了当表示空间是Lorentz空间时，由任意点产生的极限方向。特别地，我们利用无限阶元的特征向量刻画了类光极限方向。这提供了对极限根的谱透视，允许有效的计算。此外，我们描述的类空极限方向的投影Coxeter安排。
英文摘要：
Every Coxeter group admits a geometric representation as a group generated by reflections in a real vector space. In the projective representation space, limit directions are limits of injective sequences in the orbit of some base point. Limit roots are limit directions that can be obtained starting from simple roots. In this article, we study the limit directions arising from any point when the representation space is a Lorentz space. In particular, we characterize the light-like limit directions using eigenvectors of infinite-order elements. This provides a spectral perspective on limit roots, allowing for efficient computations. Moreover, we describe the space-like limit directions in terms of the projective Coxeter arrangement.
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