Reversible quaternionic hyperbolic isometries

Abstract

Let G be a group. An element g∈G is called reversible if it is conjugate to g−1 within G, and called strongly reversible if it is conjugate to g−1 by an order two element of G. Let HHn be the n-dimensional quaternionic hyperbolic space. Let PSp(n,1) be the isometry group of HHn. In this paper, we classify reversible and strongly reversible elements in Sp(n) and Sp(n,1). Also, we prove that all the elements of PSp(n,1) are strongly reversible.