Standard Lyndon loop words: weighted orders
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2024
- DOI:
- 10.48550/arXiv.2407.19939
- arXiv:
- arXiv:2407.19939
- Bibcode:
- 2024arXiv240719939K
- Keywords:
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- Mathematics - Representation Theory;
- Mathematics - Combinatorics;
- Mathematics - Quantum Algebra
- E-Print:
- v1: 30pp, comments are welcome! arXiv admin note: text overlap with arXiv:2102.11269