Representation theory of hereditary artin algebras of finite representation type

Let $H$ be a hereditary artin algebra of finite representation type. We first determine all hammocks in the Auslander-Reiten quiver $\text{GaH}$ of $\text{mmod}H$, the category of finitely generated left $H$-modules. This enables us to obtain an effective method to construct $\text{GaH}$ by simply viewing the ext-quiver of $H$. As easy applications, we compute the numbers of non-isomorphic indecomposable objects in $\text{mmod}H$ and the associated cluster category ${\mathcal{C}}_H$, as well as the nilpotencies of the radicals of $\text{mmod}H,$ $D^b(\text{mmod}H)$ and ${\mathcal{C}}_H$.