Quantum double Schubert polynomials represent Schubert classes

Details Quantum double Schubert polynomials represent Schubert classes Quantum double Schubert polynomials represent Schubert classes

2011-08-24

arxiv.org/abs/1108.4958v1

Mathematics

Combinatorics

14 pages

Scientific paper

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.

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