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Quantum double Schubert polynomials represent Schubert classes

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.

preprint2011arXivOpen access
Thomas LamMark Shimozono
math.COmath.AG
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Thomas LamMark Shimozono

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