On the Relation of Extended Affine Weyl Groups and Indefinite Weyl Groups

Extended affine Weyl groups are the Weyl groups of root systems of a new class of Lie algebras called extended affine Lie algebras. In this paper we show that a (reduced) extended affine Weyl group is the homomorphic image of some indefinite Kac–Moody Weyl group where the homomorphism and its kernel are given explicitly.