Mathematical Research Letters

Volume 20 (2013)

Number 3

Coxeter groups are not higher rank arithmetic groups

Pages: 567 – 580

DOI: http://dx.doi.org/10.4310/MRL.2013.v20.n3.a13

Author

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

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

Keywords

Coxeter groups, irreducible lattices, orthogonal groups, superrigidity

2010 Mathematics Subject Classification

Primary 20F55. Secondary 22E40.

Full Text (PDF format)