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

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- by Christopher J. Brooks, Abraham Martín del Campo and Frank Sottile PDF
- Trans. Amer. Math. Soc.
**367**(2015), 4183-4206 Request permission

## 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.## References

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## Additional Information

**Christopher J. Brooks**- Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112-0090
- Email: cbrooks@math.utah.edu
**Abraham Martín del Campo**- Affiliation: Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria
- ORCID: 0000-0003-0369-0652
- Email: abraham.mc@ist.ac.at
**Frank Sottile**- Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
- MR Author ID: 355336
- ORCID: 0000-0003-0087-7120
- Email: sottile@math.tamu.edu
- Received by editor(s): May 14, 2013
- Published electronically: November 24, 2014
- Additional Notes: This research was supported in part by NSF grant DMS-915211 and the Institut Mittag-Leffler
- © Copyright 2014
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc.
**367**(2015), 4183-4206 - MSC (2010): Primary 14N15, 05E15
- DOI: https://doi.org/10.1090/S0002-9947-2014-06192-8
- MathSciNet review: 3324924