Geodesic
Generalisations of the Tits representation
The electronic journal of combinatorics, Tome 15 (2008)
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We construct a group $K_n$ with properties similar to infinite Coxeter groups. In particular, it has a geometric representation featuring hyperplanes, simplicial chambers and a Tits cone. The generators of $K_n$ are given by $2$-element subsets of $\{0,\ldots,n\}$. We provide some generalities to deal with groups like these. We give some easy combinatorial results on the finite residues of $K_n$, which are equivalent to certain simplicial real central hyperplane arrangements.
DOI : 10.37236/858
Classification : 20F55, 20C15, 20E42, 51E24, 52C35, 20F05
Mots-clés : infinite Coxeter groups, Tits cones, Tits representations, hyperplane arrangements, buildings, linear representations, fully colored graphs 
@article{10_37236_858,
     author = {Daan Krammer},
     title = {Generalisations of the {Tits} representation},
     journal = {The electronic journal of combinatorics},
     year = {2008},
     volume = {15},
     doi = {10.37236/858},
     zbl = {1171.20027},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/858/}
}
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Daan Krammer. Generalisations of the Tits representation. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/858

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