Geodesic
Cayley Graph Characterization of Geometric Reflections
Saeid Azam1, 2 ; Fatemeh Parishani1
1Department of Mathematics, University of Isfahan, Isfahan, Iran
2School of Mathematics, Institute for Research in Fundamental Sciences, Isfahan, Iran
Journal of Lie Theory, Tome 31 (2021) no. 2, pp. 413-438

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 17B67 20F55, 05C25
Mots-clés : Extended affine Weyl groups, Cayley graphs, Coxeter groups, normalized darts, reflections

Saeid Azam  1 , 2   ; Fatemeh Parishani  1

1 Department of Mathematics, University of Isfahan, Isfahan, Iran
2 School of Mathematics, Institute for Research in Fundamental Sciences, Isfahan, Iran 
Saeid Azam; Fatemeh Parishani. Cayley Graph Characterization of Geometric Reflections. Journal of Lie Theory, Tome 31 (2021) no. 2, pp. 413-438. http://geodesic.mathdoc.fr/item/JOLT_2021_31_2_a6/
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     author = {Saeid Azam and Fatemeh Parishani},
     title = {Cayley {Graph} {Characterization} of {Geometric} {Reflections}},
     journal = {Journal of Lie Theory},
     pages = {413--438},
     year = {2021},
     volume = {31},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2021_31_2_a6/}
}
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