# Simply Laced Extended Affine Weyl Groups (A Finite Presentation)

### Saeid Azam

University of Isfahan, Iran### Valiollah Shahsanaei

University of Isfahan, Iran

## Abstract

Extended affine Weyl groups are the Weyl groups of extended affine root systems. Finite presentations for extended affine Weyl groups are known only for nullities $≤2$, where for nullity $2$ there is only one known such presentation. We give a ﬁnite presentation for the class of simply laced extended affine Weyl groups. Our presentation is nullity free if rank $>1$ and for rank $1$ it is given for nullities $≤3$. The generators and relations are given uniformly for all types, and for a given nullity they can be read from the corresponding ﬁnite Cartan matrix and the semilattice involved in the structure of the root system.

## Cite this article

Saeid Azam, Valiollah Shahsanaei, Simply Laced Extended Affine Weyl Groups (A Finite Presentation). Publ. Res. Inst. Math. Sci. 43 (2007), no. 2, pp. 403–424

DOI 10.2977/PRIMS/1201011788