I'll give some examples of pairs of centralizer algebras acting on a space and explain how the representation theory of the algebras relate to each other. In particular, I will show how this relationship is used to construct a combinatorial graph, called a Bratteli diagram, which can be used to encode the dimensions of the irreducible representations. I'll show how this graph is constructed for several examples of pairs of algebras and, in particular, the Tenabe algebra. I'll show how it is related to set valued tableaux and I'll talk about the problem of finding a tableau model for the irreducible Tenabe modules and the goal of constructing the irreducible representations with the tableaux as a basis.