Standard Lyndon loop words: weighted orders
Representation Theory
2025-02-24 v2 Combinatorics
Quantum Algebra
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.
Cite
@article{arxiv.2407.19939,
title = {Standard Lyndon loop words: weighted orders},
author = {Severyn Khomych and Nazar Korniichuk and Kostiantyn Molokanov and Alexander Tsymbaliuk},
journal= {arXiv preprint arXiv:2407.19939},
year = {2025}
}
Comments
v2: 32 pages, minor corrections, details added. v1: 30 pages, comments are welcome! arXiv admin note: text overlap with arXiv:2102.11269