Extended affine Weyl groups: Presentation by conjugation via integral collection

TL;DR

This paper establishes criteria and provides a computational method to determine when extended affine Weyl groups admit a presentation by conjugation, especially focusing on non-simply laced cases.

Contribution

It introduces necessary and sufficient conditions and a computational tool for the presentation by conjugation in extended affine Weyl groups, advancing understanding of their algebraic structure.

Findings

Criteria for existence of presentation by conjugation

A computational tool for verification

Determination for a large class of groups

Abstract

We give several necessary and sufficient conditions for the existence of {\it the presentation by conjugation} for a non-simply laced extended affine Weyl group. We invent a computational tool by which one can determine simply the existence of the presentation by conjugation for an extended affine Weyl group. As an application, we determine the existence of the presentation by conjugation for a large class of extended affine Weyl groups.