A Note on Quaternionic Hyperbolic Ideal Triangle Groups

摘要

In this paper, the quaternionic hyperbolic ideal triangle groups are parametrized by a real one-parameter family {phi(s) : s is an element of R}. The indexing parameter s is the tangent of the quaternionic angular invariant of a triple of points in partial derivative H-H(2) forming this ideal triangle. We show that if s > root 125/3, then phi(s) is not a discrete embedding, and if s <= root 35, then phi(s) is a discrete embedding.