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arXiv · 2406.05311

A quantum Murnaghan--Nakayama rule for the flag manifold

Carolina Benedetti·Nantel Bergeron·Laura Colmenarejo·Franco Saliola·Frank Sottile
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Abstract

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.

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Carolina Benedetti, Nantel Bergeron, Laura Colmenarejo, Franco Saliola, Frank Sottile. 2024-06-08. A quantum Murnaghan--Nakayama rule for the flag manifold. https://doi.org/10.5802/alco.427

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