Geng, Shengfei, The dimension vectors of indecomposable modules of cluster-tilted algebras and the Fomin-Zelevinsky denominators conjecture, Acta mathematica Sinica. English series (Print) , 28(3), 2012, pp. 581-586
The main result of this paper is that any two non-isomorphic indecomposable modules of a cluster-tilted algebra of finite representation type have different dimension vectors. As an application to cluster algebras of Types A,D,E, we give a proof of the Fomin-Zelevinsky denominators conjecture for cluster variables, namely, different cluster variables have different denominators with respect to any given cluster