We consider self-affine sets on the plane. The famous Bárány-Hochman-Rapaport and Hochman-Rapaport results give the Hausdorff dimension of these sets if the system is strongly irreducible.

We study the irreducible but not strongly irreducible case, when some linear parts are diagonal and some are antidiagonal matrices. Under some conditions, we give the dimension result in this last case.

The talk is based on our joint work with Demi Allen, Antti Kaenmaki, Daniel Prokaj and Sascha Troscheit.