Geodesic
Generalisations of the Tits representation
The electronic journal of combinatorics, Tome 15 (2008)

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Zbl arXiv EuDML
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 
Daan Krammer. Generalisations of the Tits representation. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/858
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     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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