Mathematical Research Letters

Volume 20 (2013)

Number 3

Coxeter groups are not higher rank arithmetic groups

Pages: 567 – 580



Sandip Singh (School of Mathematics, Tata Institute of Fundamental Research, Mumbai, India)


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 $\mathbb{R}$-rank $\geq 2$.


Coxeter groups, irreducible lattices, orthogonal groups, superrigidity

2010 Mathematics Subject Classification

Primary 20F55. Secondary 22E40.

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