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Paper   IPM / M / 2320
School of Mathematics
  Title:   A presentation for reduced extended affine Weyl groups
  Author(s):  S. Azam
  Status:   Published
  Journal: Comm. Algebra
  No.:  1
  Vol.:  28
  Year:  2000
  Pages:   465-488
  Supported by:  IPM
In 1985 K. Satio [Sal] introduced the concept of an extended affine Weyl group (EAWG), the Weyl group of an extended affine root system (EARS). In [A2, Section 5], we gave a presentation called "a presentation by conjugation" for the class of EAWGs of index zero, a subclass of EAWGs. In this paper we will give a presentation which we call a "generalized presentation by conjugation" for the class of reduced EAWGs. If the extended affine Weyl group is of index zero this presentation reduce to "a presentation by conjugation". Our main result states that when the nullity of the EARS is 2, these two presentation coincide that is, EAWGs of nullity 2 have "a presentation by conjugation". In [ST] another presentation for EAWGs of nullity 2 is given.

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