Unfaithful complex hyperbolic triangle groups, II: Higher order reflections

John R. Parker and Julien Paupert

Vol. 239 (2009), No. 2, 357–389

DOI: 10.2140/pjm.2009.239.357

Abstract

We consider symmetric complex hyperbolic triangle groups generated by three complex reflections through angle 2π∕p, with p ≥ 3. We restrict our attention to those groups where certain words are elliptic. Our goal is to find necessary conditions for such a group to be discrete. The main application we have in mind is that such groups are candidates for nonarithmetic lattices in SU(2,1).

Keywords

complex reflection, complex hyperbolic, lattices in SU(2,1), nonarithmetic lattice

Mathematical Subject Classification 2000

Primary: 20H10, 22E40, 51M10

Milestones

Received: 28 November 2007

Accepted: 15 October 2008

Published: 27 November 2008