On the Polytope Model and Near End node Isomorphisms of Type $A$ Kirillov--Reshetikhin Crystals
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916946531844096 |
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| author | Biswas, Dipnit Habib, Irfan |
| author_facet | Biswas, Dipnit Habib, Irfan |
| contents | We prove an inductive formula to construct a path from the highest weight element to any given vertex in the crystal graph of the polytope realization of the Kirillov-Reshetikhin crystal $KR^{i,m}$ of type $A$. For $i \leq 2$ or $i \geq n-1$, we provide explicit formulas of the same by only using the lowering crystal operators and in those cases, using these paths, we determine the explicit image of any element under the affine crystal isomorphisms between the polytope and the tableau realizations of the Kirillov-Reshetikhin crystals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19796 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Polytope Model and Near End node Isomorphisms of Type $A$ Kirillov--Reshetikhin Crystals Biswas, Dipnit Habib, Irfan Combinatorics We prove an inductive formula to construct a path from the highest weight element to any given vertex in the crystal graph of the polytope realization of the Kirillov-Reshetikhin crystal $KR^{i,m}$ of type $A$. For $i \leq 2$ or $i \geq n-1$, we provide explicit formulas of the same by only using the lowering crystal operators and in those cases, using these paths, we determine the explicit image of any element under the affine crystal isomorphisms between the polytope and the tableau realizations of the Kirillov-Reshetikhin crystals. |
| title | On the Polytope Model and Near End node Isomorphisms of Type $A$ Kirillov--Reshetikhin Crystals |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2508.19796 |