From i-boxes to signed words
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912980546879488 |
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| author | Contu, Alessandro Qin, Fan Wei, Qiaoling |
| author_facet | Contu, Alessandro Qin, Fan Wei, Qiaoling |
| contents | The combinatorics of i-boxes has recently been introduced by Kashiwara--Kim--Oh--Park in the study of cluster algebras arising from the representation theory of quantum affine algebras. In this article, we associate to each chain of i-boxes a signed word, which canonically determines a cluster seed following Berenstein--Fomin--Zelevinsky. By bridging these two different languages, we are able to provide a quick solution to the problem of explicit determining the exchange matrices associated with chains of i-boxes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06182 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From i-boxes to signed words Contu, Alessandro Qin, Fan Wei, Qiaoling Representation Theory Quantum Algebra 13F60 (Primary) The combinatorics of i-boxes has recently been introduced by Kashiwara--Kim--Oh--Park in the study of cluster algebras arising from the representation theory of quantum affine algebras. In this article, we associate to each chain of i-boxes a signed word, which canonically determines a cluster seed following Berenstein--Fomin--Zelevinsky. By bridging these two different languages, we are able to provide a quick solution to the problem of explicit determining the exchange matrices associated with chains of i-boxes. |
| title | From i-boxes to signed words |
| topic | Representation Theory Quantum Algebra 13F60 (Primary) |
| url | https://arxiv.org/abs/2507.06182 |