Galois groups of Schubert problems of lines are at least alternating Academic Article uri icon


  • 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.

published proceedings

  • Transactions of the American Mathematical Society

altmetric score

  • 1

author list (cited authors)

  • Brooks, C. J., del Campo, A. M., & Sottile, F.

citation count

  • 2

complete list of authors

  • Brooks, Christopher J||del Campo, Abraham Martín||Sottile, Frank

publication date

  • June 2015