Affine Weyl groups

Richard Kane,Peter Borwein,Jonathan Borwein

doi:10.1007/978-1-4757-3542-0_12

Affine Weyl groups

Richard Kane, Peter Borwein + Show 1 more

https://doi.org/10.1007/978-1-4757-3542-0_12

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Publication Date: Jan 1, 2001

Citations: 7

Affiliation: Western University, Simon Fraser University

#Affine Weyl Groups #Weyl Group + Show 8 more

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Abstract

We can pass from the Weyl group of a crystallographic root system and form an infinite group that has more information about the root system, and yet still possesses a structure analogous to that of the Weyl group. Notably, it has a Coxeter group structure. This group is called the affine Weyl group. Affine Weyl groups have a number of uses. They will be used in Chapter 12 to analyze subroot systems of crystallographic root systems. They are even useful for understanding ordinary Weyl groups. This will be demonstrated in §11–6.

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