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arxiv: 1108.4958 · v1 · submitted 2011-08-24 · 🧮 math.CO · math.AG

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Quantum double Schubert polynomials represent Schubert classes

Thomas Lam , Mark Shimozono
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classification 🧮 math.CO math.AG
keywords schubertquantumclassesdoublepolynomialsrepresentcohomologyequivariant
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Schubert line defects in 3d GLSMs, part II: Partial flag manifolds and parabolic quantum polynomials

    hep-th 2026-01 unverdicted novelty 7.0

    Schubert line defects in 3d GLSMs for partial flag manifolds reproduce parabolic Whitney polynomials for Schubert classes in quantum K-theory and yield new parabolic quantum Grothendieck polynomials.

  2. Schubert line defects in 3d GLSMs, part I: Complete flag manifolds and quantum Grothendieck polynomials

    hep-th 2025-12 unverdicted novelty 7.0

    Schubert line defects in 3d GLSMs for complete flag manifolds are realized as SQM quivers whose indices give quantum Grothendieck polynomials and restrict the target space to Schubert varieties.