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

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 in the same conjugacy class as the generators of Deligne-Mostow lattices. We use formal computations in SAGE to obtain the results. The code files are available on GitHub ([FPUP21]).