2006/07/06 by Saeid Azam, Azam, Saeid, Valiollah Sahsanaei +1
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Geometric and Algebraic Topology #math.QA #msc:17B67 #msc:20F55
paper · pdf · doi:10.48550/arxiv.math/0607149
a few minor corrections is made in the last page of article
arxiv created 2006/07/11 · arxiv updated 2009/12/01
There is a well-known presentation for finite and affine Weyl groups called the \it presentation by conjugation. Recently, it has been proved that this presentation holds for certain sub-classes of extended affine Weyl groups, the Weyl groups of extended affine root systems. In particular, it is shown that if nullity is ≤ 2, an A1-type extended affine Weyl group has the presentation by conjugation. We set up a general framework for the study of simply laced extended affine Weyl groups. As a result, we obtain certain necessary and sufficient conditions for an A1-type extended affine Weyl group of arbitrary nullity to have the presentation by conjugation. This gives an affirmative answer to a conjecture that there are extended affine Weyl groups which are not presented by "presentation by conjugation".