Quantum Schubert calculus for smooth Schubert divisors of Fℓ_n

2025/09/22 by Changzheng Li, Li, Changzheng, Jiayu Song +5
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #math.AG

paper · pdf · doi:10.48550/arxiv.2509.17857

openalex publication_date 2025/09/22 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

We propose to study the quantum Schubert calculus for Schubert varieties, and investigate the smooth Schubert divisors X of the complete flag variety Fl_n. We provide a Borel-type ring presentation of the quantum cohomology of X. We derive the quantum Chevalley formula for X by geometric arguments. We also show that the quantum Schubert polynomials for X are the same as that for Fl_n introduced by Fomin, Gelfand and Postnikov.

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