# Galois groups of Schubert problems of lines are at least alternating

Brooks C, Martin del Campo Sanchez A, Sottile F. 2015. Galois groups of Schubert problems of lines are at least alternating. Transactions of the American Mathematical Society. 367(6), 4183–4206.

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Author

Brooks, Christopher;
Martin del Campo Sanchez, Abraham

^{IST Austria}; Sottile, FrankDepartment

Abstract

We show that the Galois group of any Schubert problem involving lines in projective space contains the alternating group. This constitutes the largest family of enumerative problems whose Galois groups have been largely determined. Using a criterion of Vakil and a special position argument due to Schubert, our result follows from a particular inequality among Kostka numbers of two-rowed tableaux. In most cases, a combinatorial injection proves the inequality. For the remaining cases, we use the Weyl integral formulas to obtain an integral formula for these Kostka numbers. This rewrites the inequality as an integral, which we estimate to establish the inequality.

Publishing Year

Date Published

2015-06-01

Journal Title

Transactions of the American Mathematical Society

Acknowledgement

This research was supported in part by NSF grant DMS-915211 and the Institut Mittag-Leffler.

Volume

367

Issue

6

Page

4183 - 4206

IST-REx-ID

### Cite this

Brooks C, Martin del Campo Sanchez A, Sottile F. Galois groups of Schubert problems of lines are at least alternating.

*Transactions of the American Mathematical Society*. 2015;367(6):4183-4206. doi:10.1090/S0002-9947-2014-06192-8Brooks, C., Martin del Campo Sanchez, A., & Sottile, F. (2015). Galois groups of Schubert problems of lines are at least alternating.

*Transactions of the American Mathematical Society*. American Mathematical Society. https://doi.org/10.1090/S0002-9947-2014-06192-8Brooks, Christopher, Abraham Martin del Campo Sanchez, and Frank Sottile. “Galois Groups of Schubert Problems of Lines Are at Least Alternating.”

*Transactions of the American Mathematical Society*. American Mathematical Society, 2015. https://doi.org/10.1090/S0002-9947-2014-06192-8.C. Brooks, A. Martin del Campo Sanchez, and F. Sottile, “Galois groups of Schubert problems of lines are at least alternating,”

*Transactions of the American Mathematical Society*, vol. 367, no. 6. American Mathematical Society, pp. 4183–4206, 2015.Brooks, Christopher, et al. “Galois Groups of Schubert Problems of Lines Are at Least Alternating.”

*Transactions of the American Mathematical Society*, vol. 367, no. 6, American Mathematical Society, 2015, pp. 4183–206, doi:10.1090/S0002-9947-2014-06192-8.**All files available under the following license(s):**

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