Coadjoint orbits in representation theory of pro-Lie groups

TL;DR

This paper establishes a bijective correspondence between unitary irreducible representations and coadjoint orbits for a broad class of pro-Lie groups, extending classical results to more general infinite-dimensional settings.

Contribution

It introduces a new correspondence for pro-Lie groups, including infinite products of nilpotent Lie groups, broadening the scope of representation theory.

Findings

Established a one-to-one correspondence for pro-Lie groups.

Extended classical orbit method to infinite-dimensional groups.

Applicable to connected locally compact nilpotent groups.

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.