Smoothness of Schubert varieties in twisted affine Grassmannians

Abstract

We give a complete list of smooth and rationally smooth normalized Schubert varieties in the twisted affine Grassmannian associated with a tamely ramified group and a special vertex of its Bruhat–Tits building. The particular case of the quasi-minuscule Schubert variety in the quasi-split but non-split form of ${Spin}_8$ (ramified triality) provides an input needed in the article by He–Pappas–Rapoport classifying Shimura varieties with good or semi-stable reduction.