The action of a Coxeter element on an affine root system
Nathan Reading, Salvatore Stella
TL;DR
This paper extends the understanding of Coxeter element actions from finite to affine root systems, providing a detailed and uniform characterization of root orbits in the affine case.
Contribution
It develops a new, detailed, and uniform method for describing root orbits under Coxeter elements in affine root systems, building on prior finite case results.
Findings
Characterization of root orbits under Coxeter elements in affine systems
Enhanced uniformity and detail in the affine setting
Extension of finite root system results to affine case
Abstract
The characterization of orbits of roots under the action of a Coxeter element is a fundamental tool in the study of finite root systems and their reflection groups. This paper develops the analogous tool in the affine setting, adding detail and uniformity to a result of Dlab and Ringel.
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