Abstract

For all d belonging to a density-1/8 subset of the natural numbers, we give an example of a square-tiled surface conjecturally realizing the group SO* (2d) in its standard representation as the Zariski-closure of a factor of its monodromy. We prove that this conjecture holds for the first elements of this subset, showing that the group SO* (2d) is realizable for every 11 = d = 299 such that d = 3 mod 8, except possibly for d = 35 and d = 203.