Affine Standard Lyndon words: A-type

Abstract

We generalize an algorithm of Leclerc describing explicitly the bijection of Lalonde-Ram from finite to affine Lie algebras. In type $A_n^{(1)}$, 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.

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!

References in corpus (1)

• Quantum loop groups and shuffle algebras via Lyndon words

Cited by in corpus (1)

• Standard Lyndon loop words: weighted orders