Journal of Lie Theory

no. 2
Cayley Graph Characterization of Geometric Reflections
Journal of Lie Theory, Volume 31 (2021) no. 2, pp. 413-438
We combine the covering theory of graphs introduced by Malnic, Nedela and Skoviera, the notion of a Cayley graph and the theory of reflection systems in order to obtain a new characterization of geometric reflections in the theory of extended affine Weyl groups. As an immediate byproduct, we recover that an extended affine Weyl group of nullity greater than one is not a Coxeter group, with respect to any minimal generating set.
DOI: 10.5802/jolt.1178
Classification: 17B67 20F55, 05C25
Keywords: Extended affine Weyl groups, Cayley graphs, Coxeter groups, normalized darts, reflections 
@article{JOLT_2021_31_2_a6,
     author = {S. Azam and F. Parishani},
     title = {Cayley {Graph} {Characterization} of {Geometric} {Reflections}},
     journal = {Journal of Lie Theory},
     pages = {413--438},
     year = {2021},
     volume = {31},
     number = {2},
     doi = {10.5802/jolt.1178},
     zbl = {1543.20045},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1178/}
}
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%A F. Parishani
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S. Azam; F. Parishani. Cayley Graph Characterization of Geometric Reflections. Journal of Lie Theory, Volume 31 (2021) no. 2, pp. 413-438. doi: 10.5802/jolt.1178

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