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.
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Saeid Azam, Valiollah Shahsanaei, Simply Laced Extended Affine Weyl Groups (A Finite Presentation). Publ. Res. Inst. Math. Sci. 43 (2007), no. 2, pp. 403–424DOI 10.2977/PRIMS/1201011788