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arXiv · 1708.02327

Restrictions on Galois groups of Schubert problems

Robert Williams
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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 $\text{Gr}(4,9)$, 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.

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Robert Williams. 2017-08-07. Restrictions on Galois groups of Schubert problems. https://arxiv.org/abs/1708.02327

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