Representations of Deligne-Mostow lattices into

IF 0.7 4区数学 Q2 MATHEMATICS

Experimental Mathematics Pub Date : 2021-08-04 DOI:10.1080/10586458.2022.2093802

E. Falbel, I. Pasquinelli, A. Ucan-Puc

引用次数: 1

Abstract

We classify representations of a class of Deligne-Mostow lattices into PGL(3;C). In particular, we show local rigidity for the representations (of Deligne-Mostow lattices with 3-fold symmetry and of type one) where the generators we chose are of the same type as the generators of Deligne-Mostow lattices. We also show local rigidity without constraints on the type of generators for six of them and we show the existence of local deformations for a number of representations in three of them. We use formal computations in SAGE and Maple to obtain the results. The code files are available on GitHub.

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Deligne-Mostow格到

我们将一类Deligne-Mostow格的表示分类到PGL（3；C）中。特别地，我们展示了（具有3重对称性的Deligne-Mostow格和类型1的）表示的局部刚性，其中我们选择的生成元与Deligne-Mostow格的生成元具有相同的类型。我们还展示了其中六个的局部刚度，而不受生成器类型的约束，并且我们展示了其中三个的许多表示的局部变形的存在。我们使用SAGE和Maple中的形式化计算来获得结果。代码文件可在GitHub上获得。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Experimental Mathematics 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Experimental Mathematics publishes original papers featuring formal results inspired by experimentation, conjectures suggested by experiments, and data supporting significant hypotheses. Experiment has always been, and increasingly is, an important method of mathematical discovery. (Gauss declared that his way of arriving at mathematical truths was "through systematic experimentation.") Yet this tends to be concealed by the tradition of presenting only elegant, fully developed, and rigorous results. Experimental Mathematics was founded in the belief that theory and experiment feed on each other, and that the mathematical community stands to benefit from a more complete exposure to the experimental process. The early sharing of insights increases the possibility that they will lead to theorems: An interesting conjecture is often formulated by a researcher who lacks the techniques to formalize a proof, while those who have the techniques at their fingertips have been looking elsewhere. Even when the person who had the initial insight goes on to find a proof, a discussion of the heuristic process can be of help, or at least of interest, to other researchers. There is value not only in the discovery itself, but also in the road that leads to it.