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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2502.15126 |
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| _version_ | 1866929723927429120 |
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| author | Chen, Linda Kalashnikov, Elana Buckminster, Appendix by Ellis Chen, Linda Kalashnikov, Elana |
| author_facet | Chen, Linda Kalashnikov, Elana Buckminster, Appendix by Ellis Chen, Linda Kalashnikov, Elana |
| contents | Let $\bigwedge_1$ and $\bigwedge_2$ be two symmetric function algebras in independent sets of variables. We define vector space bases of $\bigwedge_1 \otimes_\mathbb{Z} \bigwedge_2$ coming from certain quivers, with vertex sets indexed by pairs of partitions. We use these vector space bases to give a positive tableau formula for Littlewood--Richardson coefficients for the product of Schubert polynomials with certain Schur polynomials in two-step flag varieties, in the spirit of the Remmel-Whitney rule for the product of two Schur polynomials in Grassmannians. This in particular covers the cases considered by the Pieri rule. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_15126 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Littlewood--Richardson rules from quivers for two-step flag varieties Chen, Linda Kalashnikov, Elana Buckminster, Appendix by Ellis Chen, Linda Kalashnikov, Elana Combinatorics Algebraic Geometry 14N15 Let $\bigwedge_1$ and $\bigwedge_2$ be two symmetric function algebras in independent sets of variables. We define vector space bases of $\bigwedge_1 \otimes_\mathbb{Z} \bigwedge_2$ coming from certain quivers, with vertex sets indexed by pairs of partitions. We use these vector space bases to give a positive tableau formula for Littlewood--Richardson coefficients for the product of Schubert polynomials with certain Schur polynomials in two-step flag varieties, in the spirit of the Remmel-Whitney rule for the product of two Schur polynomials in Grassmannians. This in particular covers the cases considered by the Pieri rule. |
| title | Littlewood--Richardson rules from quivers for two-step flag varieties |
| topic | Combinatorics Algebraic Geometry 14N15 |
| url | https://arxiv.org/abs/2502.15126 |