Staircase algebras and graded nilpotent pairs

We consider a class of finite-dimensional algebras, the so-called “Staircase algebras” parametrized by Young diagrams. We develop a complete classification of representation types of these algebras and look into finite, tame (concealed) and wild cases in more detail. Our results are translated to the setup of graded nilpotent pairs for which we prove certain finiteness conditions.