Singularities of Affine Schubert Varieties

Abstract

This paper studies the singularities of affine Schubert varieties in the affine Grassmannian (of type A_l^{(1)}). For two classes of affine Schubert varieties, we determine the singular loci; and for one class, we also determine explicitly the tangent spaces at singular points. For a general affine Schubert variety, we give partial results on the singular locus.

Keywords

• Schubert varieties
• affine Grassmannian
• loop Grassmannian