2024/06/08 by Carolina Benedetti, Nantel Bergeron, Benedetti, Carolina +7
Mathematics · #05E05 #14N15 #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2406.05311
openalex publication_date 2024/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we give a rule for the multiplication of a Schubert class by a tautological class in the (small) quantum cohomology ring of the flag manifold. As an intermediate step, we establish a formula for the multiplication of a Schubert class by a quantum Schur polynomial indexed by a hook partition. This entails a detailed analysis of chains and intervals in the quantum Bruhat order. This analysis allows us to use results of Leung--Li and of Postnikov to reduce quantum products by hook Schur polynomials to the (known) classical product.