A new description of the bicrystal $B(\infty)$ and the extended crystal
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909885171499008 |
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| author | Heo, Taehyeok |
| author_facet | Heo, Taehyeok |
| contents | We define new crystal maps on $B(\infty)$ using its polyhedral realization, and show that the crystal $B(\infty)$ equipped with the new crystal maps is isomorphic to Kashiwara's $B(\infty)$ as bicrystals. In addition, we combinatorially describe the bicrystal structure of $B(\infty)$, which is called a sliding diamond rule. Using the bicrystal structure on $B(\infty)$, we define the extended crystal and show that it is isomorphic to the extended crystal introduced by Kashiwara and Park. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12106 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A new description of the bicrystal $B(\infty)$ and the extended crystal Heo, Taehyeok Representation Theory Quantum Algebra 05E10, 17B10, 17B37 We define new crystal maps on $B(\infty)$ using its polyhedral realization, and show that the crystal $B(\infty)$ equipped with the new crystal maps is isomorphic to Kashiwara's $B(\infty)$ as bicrystals. In addition, we combinatorially describe the bicrystal structure of $B(\infty)$, which is called a sliding diamond rule. Using the bicrystal structure on $B(\infty)$, we define the extended crystal and show that it is isomorphic to the extended crystal introduced by Kashiwara and Park. |
| title | A new description of the bicrystal $B(\infty)$ and the extended crystal |
| topic | Representation Theory Quantum Algebra 05E10, 17B10, 17B37 |
| url | https://arxiv.org/abs/2504.12106 |