Peter W. Michor
The moment mapping for a unitary representation
The paper is published: Ann. Global Anal. Geometry, 8, No 3 (1990), 299--313

MSC:

22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods, {For the purely algebraic theory, See 20G05}

Abstract: For any unitary representation of an arbitrary Lie
group I construct a moment mapping from the space of smooth
vectors of the representation into the dual of the Lie algebra.
This moment mapping is equivariant and smooth. For the space of
analytic vectors the same construction is possible and leads to
a real analytic moment mapping.
Keywords: Unitary representation, moment mapping
Notes: Ann. Global Anal. Geometry, 8, No 3 (1990), 299--313,
Z 729.22016, MR 92i:58019