Galois groups of Schubert problems of lines are at least alternating

C. Brooks, A. Martin Del Campo Sanchez, F. Sottile, Transactions of the American Mathematical Society 367 (2015) 4183–4206.


Journal Article | Published | English
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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
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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/S0002-9947-2014-06192-8
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. https://doi.org/10.1090/S0002-9947-2014-06192-8
Brooks, 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 367, no. 6 (2015): 4183–4206. 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, pp. 4183–4206, 2015.
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.
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 .

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