Galois Groups of Composed Schubert Problems Institutional Repository Document uri icon

abstract

  • Two Schubert problems on possibly different Grassmannians may be composed to obtain a Schubert problem on a larger Grassmannian whose number of solutions is the product of the numbers of the original problems. This generalizes a construction discovered while classifying Schubert problems on the Grassmannian of 4-planes in C^9 with imprimitive Galois groups. We give an algebraic proof of the product formula. In a number of cases, we show that the Galois group of the composed Schubert problem is a subgroup of a wreath product of the Galois groups of the original problems, and is therefore imprimitive. We also present evidence for a conjecture that all composed Schubert problems have imprimitive Galois groups.

author list (cited authors)

  • Sottile, F., Williams, R., & Ying, L. i.

complete list of authors

  • Sottile, Frank||Williams, Robert||Ying, Li

publication date

  • October 2019