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

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arxiv 1109.2193 v1 pith:JBGL7AHT submitted 2011-09-10 math.CO math.AG

Thomas Lam , Mark Shimozono This is my paper · ORCID
classification math.COmath.AG
keywords schubertdoubleexplicitfunctionsk-doublelatticepolynomialsquantum
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We show that the k-double Schur functions defined by the authors, and the quantum double Schubert polynomials studied by Kirillov and Maeno and by Ciocan-Fontanine and Fulton, can be obtained from each other by an explicit rational substitution. The main new ingredient is an explicit computation of Kostant's solution to the Toda lattice in terms of equivariant Schubert classes.

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  1. Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian

    math.RT 2025-05 conditional novelty 7.0 of 10

    The authors explicitly realize the equivariant K-Peterson map for SL_n by a rational substitution and prove a factorization formula for K-theoretic double k-Schur functions.

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