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Home > Vol 28, No 4 (2008)

Saeid Azam and Valiollah Shahsanaei

University of Isfahan The Center for Excellence in Mathematics P.O. Box 81745-163 Darvaze-shiraz Isfahan Iran

It is known that elliptic Weyl groups, extended affine Weyl groups of nullity 2, have a finite presentation called the generalized Coexter presentation. Similar to the finite and affine case this presentation is obtained by assigning a Dynkin diagram to the root system. Then there is a prescription to read the generators and relations from the diagram. Recently a similar presentation is given for simply laced extended affine Weyl groups of nullity 3 and rank>1. Employing a new method, we complete this work by giving a similar presentation for nullity 3 extended affine Weyl groups of type A ₁.

1. Allison, B., Azam, S., Berman, S., Gao, Y., Pianzola, A.: Extended affine Lie algebras and their root systems. Mem. Am. Math. Soc. 603, 1-122 (1997)
2. Azam, S.: Nonreduced extended affine Weyl groups. J. Algebra 269, 508-527 (2003)
3. Azam, S.: Extended affine root systems. J. Lie Theory 12(2), 515-527 (2002)
4. Azam, S.: Extended affine Weyl Groups. J. Algebra 214, 571-624 (1999)
5. Azam, S.: Nonreduced extended affine root systems of nullity
3. Commun. Algebra 25, 3617-3654 (1997)
6. Azam, S., Shahsanaei, V.: Simply laced extended affine Weyl groups (a finite presentation). Publ. Res. Inst. Math. Sci. 43, 403-424 (2007)
7. Azam, S., Shahsanaei, V.: On the presentations of extended affine Weyl groups, RIMS Kyoto Univ. (to appear)
8. Azam, S., Shahsanaei, V.: Presentation by conjugation for A1 type extended affine Weyl groups. J. Algebra (to appear)
9. Moody, R.V., Shi, Z.: Toroidal Weyl groups. Nova J. Algebra Geom. 11, 317-337 (1992)
10. Saito, K.: Extended affine root systems 1 (Coxeter transformations). RIMS Kyoto Univ. 21, 75-179 (1985)
11. Saito, K., Takebayashi, T.: Extended affine root systems III (elliptic Weyl groups). Publ. Res. Inst.