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Paper IPM / M / 8428  


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.
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