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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | https://arxiv.org/abs/2508.19066 |
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| _version_ | 1866918130899484672 |
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| author | Francone, Luca Leclerc, Bernard |
| author_facet | Francone, Luca Leclerc, Bernard |
| contents | We give an introduction to our results on cluster structures for schemes of $(G,c)$-bands emphasizing their connections with seminal works of Frenkel and Reshetikhin in the 90's. In particular we construct using $(G,c)$-bands a discrete analogue of the difference Miura transformation of the loop group $LG$, and we show that it calculates the $q$-characters of the finite-dimensional representations of the quantum affine algebra $U_q(\widehat{\mathfrak{g}})$ of the same $A$, $D$, $E$ type as $G$, thus verifying a conjecture of Frenkel and Reshetikhin. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19066 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An introduction to $(G,c)$-bands Francone, Luca Leclerc, Bernard Representation Theory Quantum Algebra Rings and Algebras 13F60, 20G05, 17B37 We give an introduction to our results on cluster structures for schemes of $(G,c)$-bands emphasizing their connections with seminal works of Frenkel and Reshetikhin in the 90's. In particular we construct using $(G,c)$-bands a discrete analogue of the difference Miura transformation of the loop group $LG$, and we show that it calculates the $q$-characters of the finite-dimensional representations of the quantum affine algebra $U_q(\widehat{\mathfrak{g}})$ of the same $A$, $D$, $E$ type as $G$, thus verifying a conjecture of Frenkel and Reshetikhin. |
| title | An introduction to $(G,c)$-bands |
| topic | Representation Theory Quantum Algebra Rings and Algebras 13F60, 20G05, 17B37 |
| url | https://arxiv.org/abs/2508.19066 |