Coadjoint orbits in representation theory of pro-Lie groups

2017/09/15 by Daniel Beltiţă, Beltita, Daniel, Amel Zergane +1
Mathematics · #22A25 (Primary) 22A10 #22D10 #22D25 (Secondary) #Advanced Algebra and Geometry #Advanced Operator Algebra Research #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1709.05102

openalex publication_date 2017/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a one-to-one correspondence between equivalence classes of unitary irreducible representations and coadjoint orbits for a class of pro-Lie groups including all connected locally compact nilpotent groups and arbitrary infinite direct products of nilpotent Lie groups.

Related

• Amenability and representation theory of pro-Lie groups
• Coadjoint orbits of stepwise square integrable representations
• Admissible coadjoint orbits for compact Lie groups
• Lie supergroups, unitary representations, and invariant cones
• Hermitian flag manifolds and orbits of the Euclidean group