Extremality of Quaternionic Jørgensen Inequality

Abstract

Let $\mathrm{SL}(2,\mathbb{H})$ be the group of $2\times 2$ quaternionic matrices with Dieudonné determinant $1$. The group $\mathrm{SL}(2,\mathbb{H})$ acts on the five dimensional hyperbolic space by isometries. We investigate extremality of Jørgensen type inequalities in $\mathrm{SL}(2,\mathbb{H})$. Along the way, we derive Jørgensen type inequalities for quaternionic Möbius transformations which extend earlier inequalities obtained by Waterman and Kellerhals.

arXiv commentminor revisions, added references, introduction reorganized