Representations of Deligne-Mostow lattices into PGL(3, C)

E Falbel; I Pasquinelli; A Ucan-Puc

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arXiv · 2108.02631

Representations of Deligne-Mostow lattices into PGL(3, C)

E Falbel·I Pasquinelli·A Ucan-Puc

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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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BibTeX RIS

E Falbel, I Pasquinelli, A Ucan-Puc. 2021-08-04. Representations of Deligne-Mostow lattices into PGL(3, C). https://arxiv.org/abs/2108.02631

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