  We prove that the finitistic dimension conjecture, the Gorenstein Symmetry
Conjecture, the Wakamatsu-tilting conjecture and the generalized Nakayama
conjecture hold for artin algebras which can be realized as endomorphism
algebras of modules over representation-finite algebras. Note it is a question
whether or not all artin algebras have such realizations. It was also shown
that if every quasi-hereditary algebras has a left idealized extension which is
a monomial algebra or an algebra whose representation dimension is not more
than 3, then the finitistic dimension conjecture holds.
