A quantum Murnaghan--Nakayama rule for the flag manifold
Carolina Benedetti, Nantel Bergeron, Laura Colmenarejo, Franco Saliola, Frank Sottile
公開日: 2024/6/8
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.