Coxeter Groups are not higher rank Arithmetic Groups

Sandip Singh

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arXiv · 1208.6569

Coxeter Groups are not higher rank Arithmetic Groups

Sandip Singh

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Abstract

Let W be an irreducible finitely generated Coxeter group. The geometric representation of W in GL(V) provides a discrete embedding in the orthogonal group of the Tits form (the associated bilinear form of the Coxeter group). If the Tits form of the Coxeter group is non-positive and non-degenerate, the Coxeter group does not contain any finite index subgroup isomorphic to an irreducible lattice in a semisimple group of R-rank greater or equal to 2.

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Sandip Singh. 2014-04-11. Coxeter Groups are not higher rank Arithmetic Groups. https://arxiv.org/abs/1208.6569

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