Restrictions on Galois groups of Schubert problems

2017/08/07 by Robert Lee Williams, Williams, Robert
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1708.02327

openalex publication_date 2017/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Galois group of a Schubert problem encodes some structure of its set of solutions. Galois groups are known for a few infinite families and some special problems, but what permutation groups may appear as a Galois group of a Schubert problem is still unknown. We expand the list of Schubert problems with known Galois groups by fully exploring the Schubert problems on Gr(4,9), the smallest Grassmannian for which they are not currently known. We also discover sets of Schubert conditions for any sufficiently large Grassmannian that imply the Galois group of a Schubert problem is much smaller than the full symmetric group.

Related

• Classification of Schubert Galois groups in Gr(4,9)
• Galois Groups of Composed Schubert Problems
• Double transitivity of Galois Groups in Schubert Calculus of\n Grassmannians
• Galois groups of Schubert problems of lines are at least alternating
• Galois groups of Schubert problems via homotopy computation