Presentation by conjugation for $A_1$-type extended affine Weyl groups
| dc.creator | Azam, Saeid | |
| dc.creator | Sahsanaei, Valiollah | |
| dc.date | 2006-07-06 | |
| dc.date | 2006-07-11 | |
| dc.date.accessioned | 2026-07-07T07:18:05Z | |
| dc.date.available | 2026-07-07T07:18:05Z | |
| dc.description | 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 $\leq 2$, an $A_1$-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 $A_1$-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". | |
| dc.description | a few minor corrections is made in the last page of article | |
| dc.identifier | https://arxiv.org/abs/math/0607149 | |
| dc.identifier | http://arxiv.org/abs/math/0607149 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/114175 | |
| dc.subject | Quantum Algebra | |
| dc.subject | 17B67; 20F55 | |
| dc.title | Presentation by conjugation for $A_1$-type extended affine Weyl groups | |
| dc.type | text |