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

TL;DR

This paper establishes a criterion for the normality of Schubert varieties in twisted affine Grassmannians based on algebraic fundamental groups, with applications to local models in various characteristics and classifications for specific cases.

Contribution

It introduces a new normality criterion for Schubert varieties in twisted affine Grassmannians and applies it to classify certain local models and cases.

Findings

Normality criterion based on algebraic fundamental groups

Classification of normal Pappas-Zhu local models at special levels

Normality results in small positive characteristic

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.