From quantum Schubert polynomials to k-Schur functions via the Toda lattice

2010/10/19 by Thomas Lam, Mark Shimozono, Lam, Thomas +1 · 3 citations
Chemistry · Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Molecular spectroscopy and chirality #math.AG #math.CO

paper · pdf · doi:10.48550/arxiv.1010.4047

11 pages, minor changes, acknowledgments added

openalex publication_date 2010/10/19 · arxiv created 2010/10/26 · arxiv updated 2010/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that Lapointe-Lascoux-Morse k-Schur functions (at t=1) and Fomin-Gelfand-Postnikov quantum Schubert polynomials can be obtained from each other by a rational substitution. This is based upon Kostant's solution of the Toda lattice and Peterson's work on quantum Schubert calculus.

Cited by

• Raising operators and the Littlewood-Richardson polynomials
• Weighted K-k-Schur functions and their application to the K-k-Schur alternating conjecture
• Relativistic Toda lattice and equivariant K-homology of affine Grassmannian

Related

• From double quantum Schubert polynomials to k-double Schur functions via the Toda lattice
• Quantum Schubert polynomials and quantum Schur functions
• Quantum multiplication of Schur polynomials
• A quantum Murnaghan--Nakayama rule for the flag manifold
• Quantum Schubert calculus for smooth Schubert divisors of Fℓ_n