Normality of Schubert varieties in affine Grassmannians II: The tamely ramified case

Abstract

We prove a criterion for the normality of Schubert varieties in twisted affine Grassmannians in terms of the order of the algebraic fundamental group of a certain Levi subgroup, in particular in small positive characteristic. As an application, we obtain a similar normality criterion for local models in both equal and mixed characteristic. In particular, we give a classification of normal Pappas-Zhu local models at absolutely special level as well as for adjoint groups of rank 1.