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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2202.06004 |
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| _version_ | 1866914709690646528 |
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| author | Gunna, Ajeeth Scrimshaw, Travis |
| author_facet | Gunna, Ajeeth Scrimshaw, Travis |
| contents | We introduce the edge Schur functions $E^λ$ that are defined as a generating series over edge labeled tableaux. We formulate $E^λ$ as the partition function for a solvable lattice model, which we use to show they are symmetric polynomials and derive a Cauchy-type identity with factorial Schur polynomials. Finally, we give a crystal structure on edge labeled tableau to give a positive Schur polynomial expansion of $E^λ$ and show it intertwines with an uncrowding algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_06004 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Integrable systems and crystals for edge labeled tableaux Gunna, Ajeeth Scrimshaw, Travis Combinatorics Quantum Algebra Representation Theory 05A19, 05E05, 82B23, 14M15 We introduce the edge Schur functions $E^λ$ that are defined as a generating series over edge labeled tableaux. We formulate $E^λ$ as the partition function for a solvable lattice model, which we use to show they are symmetric polynomials and derive a Cauchy-type identity with factorial Schur polynomials. Finally, we give a crystal structure on edge labeled tableau to give a positive Schur polynomial expansion of $E^λ$ and show it intertwines with an uncrowding algorithm. |
| title | Integrable systems and crystals for edge labeled tableaux |
| topic | Combinatorics Quantum Algebra Representation Theory 05A19, 05E05, 82B23, 14M15 |
| url | https://arxiv.org/abs/2202.06004 |