Unfaithful complex hyperbolic triangle groups, III: Arithmeticity and commensurability

Julien Paupert

Vol. 245 (2010), No. 2, 359–372

DOI: 10.2140/pjm.2010.245.359

Abstract

We prove that the so-called sporadic complex reflection triangle groups in SU(2,1) are all nonarithmetic but one, and that they are not commensurable to Mostow or Picard lattices (with a small list of exceptions). This provides an infinite list of potential new nonarithmetic lattices in SU(2,1).

Keywords

nonarithmetic lattices, complex reflection groups, complex hyperbolic geometry

Mathematical Subject Classification 2000

Primary: 20H10, 22E40, 51M10

Milestones

Received: 23 February 2009

Accepted: 5 May 2009

Published: 1 April 2010