2007/12/18 by Sara Billey, Billey, Sara C., Stephen Α. Mitchell +1 · 1 citation
Mathematics · #05E15 #14M15 #22E67 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.0712.2871
openalex publication_date 2007/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a simply-connected simple compact Lie group over the complex numbers. The affine Grassmannian is a projective ind-variety, homotopy-equivalent to the loop space of G and closely analogous to a maximal flag variety of the classical Grassmannian manifold. It has a Schubert cell decomposition indexed by the coroot lattice or equivalently by the minimal length coset representatives for the affine Weyl group modulo the Weyl group for G. The closure of an affine Schubert cell is a finite dimensional projective variety that we call an affine Schubert variety. In this paper we completely determine the smooth and palindromic (rationally smooth) affine Schubert varieties.