Classification of Schubert Galois groups in Gr(4,9)

Abraham Martin del Campo; Frank Sottile; Robert Williams

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arXiv · 1902.06809

Classification of Schubert Galois groups in Gr(4,9)

Abraham Martin del Campo·Frank Sottile·Robert Williams

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Abstract

We classify Schubert problems in the Grassmannian of 4-planes in 9-dimensional space by their Galois groups. Of the 31,806 essential Schubert problems in this Grassmannian, there are only 149 whose Galois group does not contain the alternating group. We identify the Galois groups of these 149 -- each is an imprimitive permutation group. These 149 fall into two families according to their geometry. This study suggests a possible classification of Schubert problems whose Galois group is not the full symmetric group, and it begins to establish the inverse Galois problem for Schubert calculus.

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Abraham Martin del Campo, Frank Sottile, Robert Williams. 2019-02-18. Classification of Schubert Galois groups in Gr(4,9). https://arxiv.org/abs/1902.06809

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