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

TL;DR

This paper completes the classification of certain Deligne-Mostow lattice representations into PGL(3,C), establishing local rigidity for specific generator types using computational algebra tools.

Contribution

It finalizes the classification of type preserving representations of Deligne-Mostow lattices into PGL(3,C) and proves local rigidity for key cases.

Findings

Complete classification of representations achieved.

Local rigidity established for specific generator types.

Computational methods used for verification.

Abstract

We complete the classification of type preserving representations of Deligne-Mostow lattices with 3-fold symmetry into PGL(3,C) started in arXiv:2003.06466. In particular, we show local rigidity for all the representations where the generators we chose are of the same type as the generators of the Deligne-Mostow lattices. We use formal computations in SAGE and MAPLE to obtain the results. The code files are available on GitHub.