A presentation for reduced extended affine weyl groups

Presentation by conjugation for A1-type extended affine Weyl groups

“…Using this criterion it is then easy to show that if ν 3, the Weyl groups of all extended affine root systems of type A 1 have the presentation by conjugation except only one root system, namely the one of index 7 which happens in nullity 3 (Corollary 4.2). This in particular gives an affirmative answer to a conjecture due to S. Azam [A3,Remark 3.14] that certain extended affine Weyl groups of type A 1 may not have the presentation by conjugation (see Remark 5.21).…”

“…2 Remark 5.21. (i) In [A3,Remark 2.14] the author, by suggesting an example, has conjectured that certain extended affine Weyl groups may not have the presentation by conjugation. The Corollaries 5.17 and 5.18, give an affirmative answer to this conjecture.…”

“…For the study of extended affine root systems and extended affine Weyl groups we refer the reader to [MS,Sa,AABGP,A1,A2,A3,A4,SaT,T,AS1,AS2]. The authors would like to thank A. Abdollahi for a fruitful discussion which led to the proof of crucial Lemma 5.1.…”

Classification of irreducible integrable representations for the full toroidal lie algebras

“…Then (·|·) defined above is W-invariant. See [1,2] for some interesting results on Weyl groups in the context of Toroidal Lie-algebras (or more generally the Extended Affine Lie-algebras).…”

Extended Affine Weyl Groups: Presentation by Conjugation via Integral Collection

“…• finite and affine Weyl groups, (see [St] and [MP,Proposition 5.3.3], • simply laced extended affine Weyl groups of rank > 1 (see [K, Theorem, III.1.14]), • extended affine Weyl groups of index zero, including extended affine Weyl groups of types F 4 and G 2 (see [A4,Theorem,5.15]), • nullity 2 extended affine Weyl groups of types A 1 , B ℓ , C ℓ (see [A3,Theorem 3.1]),…”