Spherical Harmonics on the Heisenberg Group

Abstract

H1. Equip ℝ3 with the group law(1.1)where (z, t) stands for (x, y, t). This is a nilpotent Lie group, usually referred to as the first Heisenberg group, H1. In general Hk denotes ℝ2k+1 equipped with a similar group law, namely