On the representation theory of the Fuss-Catalan algebras

Throughout this thesis, we study the representation theory of the Fuss-Catalan algebras, $FC_{2,n}(a, b)$. We prove that these algebras are cellular and we define their
cellular basis. In addition, we prove that they form a tower of recollement, and
hence, they are quasi-hereditary. By calculating the Gram determinants of certain
cell modules for the Fuss-Catalan algebras, we determine when these algebras are
not semisimple. Finally, we end with defining homomorphisms between specified cell modules.