Quantum bumpless pipe dreams

Le, Tuong  ; Ouyang, Shuge ; Tao, Leo ; Restivo, Joseph ; Zhang, Angelina

Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e28

Résumé

Schubert polynomials are polynomial representatives of Schubert classes in the cohomology of the complete flag variety and have a combinatorial formulation in terms of bumpless pipe dreams. Quantum double Schubert polynomials are polynomial representatives of Schubert classes in the torus-equivariant quantum cohomology of the complete flag variety, but no analogous combinatorial formulation had been discovered. We introduce a generalization of the bumpless pipe dreams called quantum bumpless pipe dreams, giving a novel combinatorial formula for quantum double Schubert polynomials as a sum of binomial weights of quantum bumpless pipe dreams. We give a bijective proof for this formula by showing that the sum of binomial weights satisfies a defining transition equation.

Détail

DOI : 10.1017/fms.2024.112

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