Standard Lyndon loop words: weighted orders
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866916624691363840 |
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| author | Khomych, Severyn Korniichuk, Nazar Molokanov, Kostiantyn Tsymbaliuk, Alexander |
| author_facet | Khomych, Severyn Korniichuk, Nazar Molokanov, Kostiantyn Tsymbaliuk, Alexander |
| contents | We generalize the study of standard Lyndon loop words from [A.Negut, A.Tsymbaliuk, "Quantum loop groups and shuffle algebras via Lyndon words", Adv. Math. 439 (2024), Paper No. 109482] to a more general class of orders on the underlying alphabet, as suggested in Remark 3.15 of loc.cit. The main new ingredient is the exponent-tightness of these words, which also allows to generalize the construction of PBW bases of the untwisted quantum loop algebra via the combinatorics of loop words. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19939 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Standard Lyndon loop words: weighted orders Khomych, Severyn Korniichuk, Nazar Molokanov, Kostiantyn Tsymbaliuk, Alexander Representation Theory Combinatorics Quantum Algebra We generalize the study of standard Lyndon loop words from [A.Negut, A.Tsymbaliuk, "Quantum loop groups and shuffle algebras via Lyndon words", Adv. Math. 439 (2024), Paper No. 109482] to a more general class of orders on the underlying alphabet, as suggested in Remark 3.15 of loc.cit. The main new ingredient is the exponent-tightness of these words, which also allows to generalize the construction of PBW bases of the untwisted quantum loop algebra via the combinatorics of loop words. |
| title | Standard Lyndon loop words: weighted orders |
| topic | Representation Theory Combinatorics Quantum Algebra |
| url | https://arxiv.org/abs/2407.19939 |