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Extended Affine Weyl Groups

โœ Scribed by Saeid Azam

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
370 KB
Volume
214
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

In this paper we study the Weyl groups of reduced extended affine root systems, the root systems of extended affine Lie algebras. We start by describing the extended affine Weyl group as a semidirect product of a finite Weyl group and a Heisenberg-like normal subgroup. This provides a unique expression for the Weyl ลฝ . group elements in terms of some naturally arisen transformations which is crucial in the further study of extended affine Weyl groups. We use this to give a presentation, called a presentation by conjugation, for an important subclass of extended affine Weyl groups. Using a new notion, called the index which is an invariant of the extended affine root systems, we show that one of the important ลฝ . features of finite and affine root systems related to Weyl group holds for the class of extended affine root systems.

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