The Classification of the Epimorphisms from the Artin-Tits groups of type $A(\widetilde{A}_{n})$ to $W(\widetilde{A}_{n})$

TL;DR

This paper provides a comprehensive classification of epimorphisms from affine Artin-Tits groups of type A tilde to their associated Coxeter groups, enhancing understanding of their algebraic structure.

Contribution

It offers the first complete classification of epimorphisms from affine Artin-Tits groups of type A tilde to their Coxeter groups.

Findings

Complete classification of epimorphisms for all n ≥ 1

Clarifies the structure of these group homomorphisms

Facilitates further algebraic and geometric analysis of these groups

Abstract

We present a complete classification for the epimorphisms from the affine Artin-Tits groups $A(\widetilde{A}_{n})$ to the corresponding Coxeter groups $W(\widetilde{A}_{n})$, for $n\geq 1$.