Crystal Chute Moves on Pipe Dreams
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916588220841984 |
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| author | Gold, Sarah Milićević, Elizabeth Sun, Yuxuan |
| author_facet | Gold, Sarah Milićević, Elizabeth Sun, Yuxuan |
| contents | Schubert polynomials represent a basis for the cohomology of the complete flag variety and thus play a central role in geometry and combinatorics. In this context, Schubert polynomials are generating functions over various combinatorial objects, such as rc-graphs or reduced pipe dreams. By restricting Bergeron and Billey's chute moves on rc-graphs, we define a Demazure crystal structure on the monomials of a Schubert polynomial. As a consequence, we provide a method for decomposing Schubert polynomials as sums of key polynomials, complementing related work of Assaf and Schilling via reduced factorizations with cutoff, as well as Lenart's coplactic operators on biwords. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_07204 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Crystal Chute Moves on Pipe Dreams Gold, Sarah Milićević, Elizabeth Sun, Yuxuan Combinatorics Representation Theory Schubert polynomials represent a basis for the cohomology of the complete flag variety and thus play a central role in geometry and combinatorics. In this context, Schubert polynomials are generating functions over various combinatorial objects, such as rc-graphs or reduced pipe dreams. By restricting Bergeron and Billey's chute moves on rc-graphs, we define a Demazure crystal structure on the monomials of a Schubert polynomial. As a consequence, we provide a method for decomposing Schubert polynomials as sums of key polynomials, complementing related work of Assaf and Schilling via reduced factorizations with cutoff, as well as Lenart's coplactic operators on biwords. |
| title | Crystal Chute Moves on Pipe Dreams |
| topic | Combinatorics Representation Theory |
| url | https://arxiv.org/abs/2403.07204 |