Toward quantum Pieri rule for Fℓ_n via Seidel representation

2025/07/16 by Changzheng Li, Jiayu Song, Li, Changzheng +1
Mathematics · #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2507.12351

openalex publication_date 2025/07/16 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

Abstract

By using a ``quantum-to-classical" reduction formula on the Gromov-Witten invariants of flag vaireities Fℓ_n, we provide a new proof of the Seidel operator on the quantum cohomology ring QH^*(Fℓ_n). Further, we reprove a quantum Pieri rule with respect to certain special Schubert class for QH^*(Fℓ_n). Finally, we propose a concrete conjecture on the corresponding quantum Pieri rule for the quantum K-theory of Fℓ_n.

Citations

• Seidel and Pieri products in cominuscule quantum K-theory
• On Seidel representation in quantum K-theory of Grassmannians
• Pieri-type multiplication formula for quantum Grothendieck polynomials
• Euler characteristics in the quantum K-theory of flag varieties
• On equivariant quantum Schubert calculus for G/P
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• Quantum K-theory of Grassmannians
• Quantum Cohomology and Crepant Resolutions: A Conjecture
• The Crepant Resolution Conjecture
• Gromov-Witten invariants on Grassmannians
• Quantum cohomology of orthogonal Grassmannians
• Quantum cohomology of the Lagrangian Grassmannian
• Transformation formulas in Quantum Cohomology
• On D. Peterson's comparison formula for Gromov-Witten invariants
• Affine approach to quantum Schubert calculus
• On the quantum product of Schubert classes
• Cohomology ring of crepant resolutions of orbifolds
• On quantum cohomology rings of partial flag varieties
• Notes on stable maps and quantum cohomology

Related

• Seidel and Pieri products in cominuscule quantum K-theory
• On Seidel representation in quantum K-theory of Grassmannians
• Quantum Pieri rules for tautological subbundles
• Pieri-type multiplication formula for quantum Grothendieck polynomials
• An equivariant quantum Pieri rule for the Grassmannian on cylindric shapes