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Quantum Schubert polynomials and quantum Schur functions

Anatol N. Kirillov
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Abstract

We introduce the quantum multi-Schur functions, quantum factorial Schur functions and quantum Macdonald polynomials. We prove that for restricted vexillary permutations the quantum double Schubert polynomial coincides with some quantum multi-Schur function and prove a quantum analog of the Nagelsbach-Kostka and Jacobi-Trudi formulae for the quantum double Schubert polynomials in the case of Grassmannian permutations. We prove, also, an analog of the Billey-Jockusch-Stanley formula for quantum Schubert polynomials. Finally we formulate two conjectures about the structure of quantum double and quantum Schubert polynomials for 321-avoiding permutations.

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Anatol N. Kirillov. 1997-01-20. Quantum Schubert polynomials and quantum Schur functions. https://arxiv.org/abs/q-alg/9701005

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