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From quantum Schubert polynomials to $$k$$-Schur functions via the Toda lattice. (English) Zbl 1269.05113
Summary: 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 on Kostant’s solution of the Toda lattice and Peterson’s work on quantum Schubert calculus.

##### MSC:
 05E05 Symmetric functions and generalizations 14N15 Classical problems, Schubert calculus
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