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{\bf Daan Krammer }
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{\bf Generalisations of the Tits Representation}
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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.



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