Affine Standard Lyndon words: A-type
Representation Theory
2024-10-03 v2 Combinatorics
Quantum Algebra
Abstract
We generalize an algorithm of Leclerc describing explicitly the bijection of Lalonde-Ram from finite to affine Lie algebras. In type , we compute all affine standard Lyndon words for any order of the simple roots, and establish some properties of the induced orders on the positive affine roots.
Cite
@article{arxiv.2305.16299,
title = {Affine Standard Lyndon words: A-type},
author = {Yehor Avdieiev and Alexander Tsymbaliuk},
journal= {arXiv preprint arXiv:2305.16299},
year = {2024}
}
Comments
v2: final version (minor corrections, proof of Theorem 4.7 expanded, proof of Proposition 5.8 added), 39 pages. v1: 32 pages, comments are welcome!