Serial functors, Jacobson radical and representation type

It is an important problem in representation theory to relate the representation type of a k-algebra A to dimensions of finitely presented functors from mod(A) to mod(k). We prove that a string algebra is of domestic representation type if and only if the dimension of all serial functors in the associated category of finitely presented functors is finite. Using the ‘hammock approach’ we provide explicit examples of serial functors.