This research uncovers geometric reflections in extended affine Weyl groups, indicating that specific groups are not Coxeter groups.
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.
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Azam et al. (2021) studied this question.
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