On the Dual Topology of a Class of Cartan Motion Groups

Key Points

• The aim is to describe the set of equivalence classes of generic irreducible unitary representations of Cartan motion groups and their topological properties.
• Analyzing the compact Riemannian symmetric pair (G, K)
• Describing equivalence classes of unitary representations of G 0
• Determining the topology of generic admissible coadjoint orbits of G 0
• Establishing a bijection between these spaces
• The set of generic irreducible unitary representations of G 0 is precisely described.
• The topology of the space of generic admissible coadjoint orbits of G 0 has been determined.
• A homeomorphism is shown between the sets of unitary representations and coadjoint orbits.
• In rank one cases, the unitary dual is homeomorphic to the space of admissible coadjoint orbits.