H is a three-dimensional, connected, simply connected and 2-step nilpotent Lie group
, (RAHMANI, 1992; KORPINAR; TURHAN, 2011, 2012,TURHAN; KORPINAR, 2010, 2011).
Let G be a simply connected 2-step nilpotent Lie group, and let H and L be connected subgroups.
Nasrin, Criterion of proper actions for 2-step nilpotent Lie groups, Tokyo J.
Q]], in a manner directly analogous to Kirillov theory for representations of connected, simply connected nilpotent Lie groups.
This is not true in general in the case of simply connected, connected nilpotent Lie groups G, where Prim(G) is isomorphic to G, with the Fell topology.
His results show that Kirillov theory applies in a modified fashion to the representation theory of groups other than simply connected, connected nilpotent Lie groups.
Greenleaf, Representations of Nilpotent Lie Groups and their Applications, Part I, Cambridge University Press, Cambridge, U.