An inequality of Kostka numbers and Galois groups of Schubert problems Conference Paper uri icon

abstract

  • We show that the Galois group of any Schubert problem involving lines in projective space contains the alternating group. Using a criterion of Vakil and a special position argument due to Schubert, this follows from a particular inequality among Kostka numbers of two-rowed tableaux. In most cases, an easy combinatorial injection proves the inequality. For the remaining cases, we use that these Kostka numbers appear in tensor product decompositions of sl 2-modules. Interpreting the tensor product as the action of certain commuting Toeplitz matrices and using a spectral analysis and Fourier series rewrites the inequality as the positivity of an integral. We establish the inequality by estimating this integral. 2012 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France.

published proceedings

  • Discrete Mathematics and Theoretical Computer Science

author list (cited authors)

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

complete list of authors

  • Brooks, CJ||Del Campo, AM||Sottile, F

publication date

  • December 2012