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 Ž . reduced extended affine Weyl group is the homomorphic image of some indefinite Kac᎐Moody Weyl group where the homomorphism and its kern
The fundamental groups of the spaces of regular orbits of the affine weyl groups
✍ Scribed by Nguyêñ Viêt Dũng
- Publisher
- Elsevier Science
- Year
- 1983
- Tongue
- English
- Weight
- 864 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0040-9383
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
If a sequence of transitive permutation groups G of degree n have orders which are not too large (log IGI--o(n~) suttices), then the number of orbits on the power set is asymptotically 2n/]GI, and almost all of these orbits are regular. This conclusion holds in particular for primitive groups.
The main result of the paper is to get the transition formulae between the alcove form and the permutation form of w ∈ W a , where W a is an affine Weyl group of classical type. On the other hand, we get a new characterization for the alcove form of an affine Weyl group element which has a much simp