تقرير
Integrable systems and crystals for edge labeled tableaux
| العنوان: | Integrable systems and crystals for edge labeled tableaux |
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| المؤلفون: | Gunna, Ajeeth, Scrimshaw, Travis |
| المصدر: | J. Algebra, 644 (2024), pp. 152-190 |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, Mathematics - Quantum Algebra, Mathematics - Representation Theory, 05A19, 05E05, 82B23, 14M15 |
| الوصف: | We introduce the edge Schur functions $E^{\lambda}$ that are defined as a generating series over edge labeled tableaux. We formulate $E^{\lambda}$ 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 $E^{\lambda}$ and show it intertwines with an uncrowding algorithm. Comment: 29 pages, 2 figures |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1016/j.jalgebra.2023.12.031 |
| URL الوصول: | http://arxiv.org/abs/2202.06004 |
| رقم الأكسشن: | edsarx.2202.06004 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1016/j.jalgebra.2023.12.031 |
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