Extremality of quaternionic Jørgensen inequality

Abstract

Let SL(2;IH) be the group of 2 × 2 quaternionic matrices with Dieudonné determinant one. The group SL(2;IH) acts on the five dimensional hyperbolic space by isometries. We investigate extremality of Jørgensen type inequalities in SL(2;IH). Along the way, we derive Jørgensen type inequalities for quaternionic Möbius transformations which extend earlier inequalities obtained by Waterman and Kellerhals. © 2017 Hiroshima University. All rights reserved.