关于布劳表示法忠实于 Artin-Tits 群的几点评论

arXiv - MATH - Representation Theory Pub Date : 2024-08-30 DOI:arxiv-2409.00144

Asilata Bapat, Hoel Queffelec

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引用次数: 0

摘要

我们讨论了将辫状群的布劳表示的忠实性问题扩展到阿尔丁--蒂茨群的情况。我们证明了布劳表示在仿射类型 $\tilde{A_3}$ 中是不忠实的，在类型 $D_4$ 的几个有限环上也是不忠实的，我们使用了一种基于分类方法的算法方法，这种方法概括了比奇洛在类型 $A$ 以外的曲线策略。

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Some remarks about the faithfulness of the Burau representation of Artin--Tits groups

We discuss the extension of the faithfulness question for the Burau representation of braid groups to the case of Artin--Tits groups. We prove that the Burau representation is not faithful in affine type $\tilde{A_3}$, and not faithful over several finite rings in type $D_4$, using an algorithmic approach based on categorical methods that generalize Bigelow's curve strategy outside of type $A$.

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arXiv - MATH - Representation Theory

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