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 \(\mathbb{P}(\mathcal{V}_{\mathcal{N}})\rightarrow\mathbb{P}(\mathcal{V}_{\mathcal{G}})\) between their projectivized cohomological support varieties and the ranks of the tubes in their Auslander-Reiten quivers.