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Proceedings of the American Mathematical Society

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The action of a Coxeter element on an affine root system


Authors: Nathan Reading and Salvatore Stella
Journal: Proc. Amer. Math. Soc. 148 (2020), 2783-2798
MSC (2010): Primary 20F55
DOI: https://doi.org/10.1090/proc/14769
Published electronically: April 16, 2020
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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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Additional Information

Nathan Reading
Affiliation: Department of Mathematics, North Carolina State University, Raleigh, North Carolina

Salvatore Stella
Affiliation: Dipartimento di Matematica “G. Castelnuovo”, Università degli Studi di Roma “La Sapienza”, Piazzale Aldo Moro, 2, 00185 Roma, Italy
Email: stella@mat.uniroma1.it

DOI: https://doi.org/10.1090/proc/14769
Received by editor(s): August 22, 2018
Received by editor(s) in revised form: March 12, 2019, and July 13, 2019
Published electronically: April 16, 2020
Additional Notes: The first author was supported in part by NSF grants DMS-1101568 and DMS-1500949.
The second author was partially supported by NCSU, INdAM, and the ISF grant 1144/16.
Communicated by: Patricia L. Hersh
Article copyright: © Copyright 2020 Nathan Reading and Salvatore Stella