Sphericality and Smoothness of Schubert Varieties

2018/03/14 by Mahir Bilen Can, Can, Mahir Bilen, Reuven Hodges +1
Mathematics · #14M15 #14M27 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1803.05515

openalex publication_date 2018/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the action of the Levi subgroup of a parabolic subgroup that stabilizes a Schubert variety. We show that a smooth Schubert variety is a homogeneous space for a parabolic subgroup, or it has a smooth Schubert divisor. Further, we show that all smooth Schubert varieties in a (partial) flag variety of a rank two simple algebraic group are spherical.

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