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| Paper IPM / M / 2320 |
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| Abstract: | |
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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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