AR-Components of domestic finite group schemes: McKay-Quivers and Ramification

For a domestic finite group scheme, we give a direct description of the Euclidean components in its Auslander-Reiten quiver via the McKay-quiver of a finite linearly reductive subgroup scheme of $SL(2)$. Moreover, for a normal subgroup scheme $\mathcal{N}$ of a finite group scheme $\mathcal{G}$, we show that there is a connection between the ramification indices of the restriction morphism $\mathbb{P}({\mathcal{V}}_{\mathcal{N}})\to \mathbb{P}({\mathcal{V}}_{\mathcal{G}})$ between their projectivized cohomological support varieties and the ranks of the tubes in their Auslander-Reiten quivers.