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      A quantum Murnaghan--Nakayama rule for the flag manifold

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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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          Author and article information

          Journal
          07 June 2024
          Article
          2406.05311
          ec02a197-6ab0-48a6-959e-5a05fe9d58c3

          http://creativecommons.org/licenses/by-nc-sa/4.0/

          History
          Custom metadata
          05E05, 14N15
          34 pages, 16 color pictures, some text and graphic in color. Full paper with all proofs
          math.CO math.AG math.QA

          Combinatorics,Geometry & Topology,Algebra
          Combinatorics, Geometry & Topology, Algebra

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