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Polynomiality of Stretched Schubert Structure Constants and Key Coefficients

  • Per Alexandersson
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Abstract

We prove that monomial coefficients in affine families of key and Schubert polynomials are eventually polynomial. These results extend to finite products. Using M.~Watanabe's Schubert duality, we deduce that stretched Schubert structure constants are eventually polynomial. This proves a conjecture stated by I.~Pak and Z.~Slonim. We also prove that the positive key expansion of every affine-code family of Schubert polynomials eventually has fixed coefficients and affine indices. The proofs combine Demazure operators and vector partition functions with P.~Magyar's orthodontic formula and the generalized Demazure character theory of V.~Lakshmibai, P.~Littelmann, and P.~Magyar.

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Cite

BibTeXRIS
BibTeX
@misc{alexandersson2026polynomiality,
  title = {{Polynomiality of Stretched Schubert Structure Constants and Key Coefficients}},
  author = {Per Alexandersson},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.18746},
  eprint = {2607.18746},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.18746},
}
RIS
TY  - UNPB
TI  - Polynomiality of Stretched Schubert Structure Constants and Key Coefficients
AU  - Per Alexandersson
PY  - 2026
DA  - 2026/10/24
PB  - arXiv
DO  - 10.48550/arxiv.2607.18746
UR  - https://arxiv.org/abs/2607.18746
AB  - We prove that monomial coefficients in affine families of key and Schubert polynomials are eventually polynomial. These results extend to finite products. Using M.~Watanabe's Schubert duality, we deduce that stretched Schubert structure constants are eventually polynomial. This proves a conjecture stated by I.~Pak and Z.~Slonim. We also prove that the positive key expansion of every affine-code family of Schubert polynomials eventually has fixed coefficients and affine indices. The proofs combine Demazure operators and vector partition functions with P.~Magyar's orthodontic formula and the generalized Demazure character theory of V.~Lakshmibai, P.~Littelmann, and P.~Magyar.
ER  -