A quantum Murnaghan--Nakayama rule for the flag manifold
| dc.contributor.author | Benedetti, Carolina | |
| dc.contributor.author | Bergeron, Nantel | |
| dc.contributor.author | Colmenarejo, Laura | |
| dc.contributor.author | Saliola, Franco | |
| dc.contributor.author | Sottile, Frank | |
| dc.date.accessioned | 2025-04-11T18:38:30Z | |
| dc.date.available | 2025-04-11T18:38:30Z | |
| dc.date.issued | 2024-06-08 | |
| dc.description | 34 pages, 16 color pictures, some text and graphic in color. Full paper with all proofs | |
| dc.description.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. | |
| dc.description.sponsorship | The authors want to thank the Algebraic Combinatorics Working Seminar at the Fields Institute where this project started in 2016. Benedetti thanks Grant FAPA of the Faculty of Science of Universidad de Los Andes. Bergeron is partially supported by NSERC and the York Research Chair in Applied Algebra. Colmenarejo was partially supported by the AMS-Simons Travel grant. Saliola is partially supported by NSERC. Sottile is partially supported by the Simons Foundation and the National Science Foundation through grant DMS-2201005. | |
| dc.identifier.uri | https://doi.org/10.48550/arXiv.2406.05311 | |
| dc.identifier.uri | https://hdl.handle.net/10315/42894 | |
| dc.language.iso | en | |
| dc.rights | Attribution-NonCommercial-ShareAlike 4.0 International | en |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/4.0/ | |
| dc.subject | Combinatorics | |
| dc.subject | Algebraic geometry | |
| dc.subject | Quantum algebra | |
| dc.subject | 05E05 | |
| dc.subject | 14N15 | |
| dc.symplectic.subtype | Preprint | |
| dc.title | A quantum Murnaghan--Nakayama rule for the flag manifold | |
| dc.type | Preprint |