English

Quantum double Schubert polynomials represent Schubert classes

Combinatorics 2011-08-26 v1 Algebraic Geometry

Abstract

The quantum double Schubert polynomials studied by Kirillov and Maeno, and by Ciocan-Fontanine and Fulton, are shown to represent Schubert classes in Kim's presentation of the equivariant quantum cohomology of the flag variety. We define parabolic analogues of quantum double Schubert polynomials, and show that they represent Schubert classes in the equivariant quantum cohomology of partial flag varieties. For complete flags Anderson and Chen have announced a proof with different methods.

Keywords

Cite

@article{arxiv.1108.4958,
  title  = {Quantum double Schubert polynomials represent Schubert classes},
  author = {Thomas Lam and Mark Shimozono},
  journal= {arXiv preprint arXiv:1108.4958},
  year   = {2011}
}

Comments

14 pages

R2 v1 2026-06-21T18:54:53.332Z