
Journal of Lie Theory 31 (2021), No. 2, 413438 Copyright Heldermann Verlag 2021 Cayley Graph Characterization of Geometric Reflections Saeid Azam Department of Mathematics, University of Isfahan, Isfahan, Iran and: School of Mathematics, Institute for Research in Fundamental Sciences, Isfahan, Iran azam@ipm.ir Fatemeh Parishani Department of Mathematics, University of Isfahan, Isfahan, Iran f.parishani93@sci.ui.ac.ir 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. Keywords: Extended affine Weyl groups, Cayley graphs, Coxeter groups, normalized darts, reflections. MSC: 17B67 20F55; 05C25. [ Fulltextpdf (211 KB)] for subscribers only. 