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Paper   IPM / M / 8428
School of Mathematics
  Title:   Simply laced extended affine Weyl groups (a finite presentation)
  Author(s):  S. Azam (Joint with V. Shahsanaei)
  Status:   Published
  Journal: Publ. RIMS, Kyoto Univ.
  Vol.:  43
  Year:  2007
  Pages:   403-424
  Supported by:  IPM
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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