## Extended affine Weyl groups of type $A_1$.

##### J. Algebr. Comb. 28(4), 481-493 (2008)
DOI: 10.1007/s10801-007-0112-1

### Summary

Summary: It is known that elliptic Weyl groups, extended affine Weyl groups of nullity 2, have a finite presentation called the generalized Coexter presentation. Similar to the finite and affine case this presentation is obtained by assigning a Dynkin diagram to the root system. Then there is a prescription to read the generators and relations from the diagram. Recently a similar presentation is given for simply laced extended affine Weyl groups of nullity 3 and rank>1. Employing a new method, we complete this work by giving a similar presentation for nullity 3 extended affine Weyl groups of type $A _{1}$.

### Keywords/Phrases

keywords Dynkin diagram, Weyl groups, root system