Monomial bases and canonical bases for quantum affine algebras
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911693695614976 |
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| author | Shoji, Toshiaki Zhou, Zhiping |
| author_facet | Shoji, Toshiaki Zhou, Zhiping |
| contents | We construct a monomial basis of a quantum affine algebra of simply-laced type, associated to the PBW basis of Beck-Nakajima. We show that there exists a simple algorithm of computing canonical basis in terms of the monomial basis. We dsicuss the relations of the canonical basis obtained from this PBW basis with Lusztig's canonical basis constructed by using the geometry of quivers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14247 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Monomial bases and canonical bases for quantum affine algebras Shoji, Toshiaki Zhou, Zhiping Quantum Algebra 17B37, 81R50 We construct a monomial basis of a quantum affine algebra of simply-laced type, associated to the PBW basis of Beck-Nakajima. We show that there exists a simple algorithm of computing canonical basis in terms of the monomial basis. We dsicuss the relations of the canonical basis obtained from this PBW basis with Lusztig's canonical basis constructed by using the geometry of quivers. |
| title | Monomial bases and canonical bases for quantum affine algebras |
| topic | Quantum Algebra 17B37, 81R50 |
| url | https://arxiv.org/abs/2605.14247 |