Double transitivity of Galois Groups in Schubert Calculus of\n Grassmannians

2013/12/20 by Frank Sottile, Sottile, Frank, Jacob White +1 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Analytic and geometric function theory #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1312.5987

openalex publication_date 2013/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate double transitivity of Galois groups in the classical Schubert\ncalculus on Grassmannians. We show that all Schubert problems on Grassmannians\nof 2- and 3-planes have doubly transitive Galois groups, as do all Schubert\nproblems involving only special Schubert conditions. We use these results to\ngive a new proof that Schubert problems on Grassmannians of 2-planes have\nGalois groups that contain the alternating group. We also investigate the\nGalois group of every Schubert problem on Gr(4,8), finding that each Galois\ngroup either contains the alternating group or is an imprimitive permutation\ngroup and therefore fails to be doubly transitive. These imprimitive examples\nshow that our results are the best possible general results on double\ntransitivity of Schubert problems.\n

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• On the irreducibility and monodromy of Tutte polynomials
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