A momentum map for the Heisenberg group
Richard Cushman
TL;DR
This paper explores the momentum map for the Heisenberg group, classifies its coadjoint orbits, and links the associated cocycle to the modulus of these orbits, providing a representation-theoretic perspective.
Contribution
It introduces a classification of coadjoint orbits for the Heisenberg group and relates the momentum map cocycle to orbit moduli with a new representation-theoretic interpretation.
Findings
Coadjoint orbits of the Heisenberg group are classified.
The cocycle of the momentum map equals the modulus of a coadjoint orbit.
A representation-theoretic description of the orbit modulus is provided.
Abstract
These notes treat a momentum map associated to the Heisenberg group. We classify the coadjoint orbits of the Heisenberg group and show that the cocycle associated to the momentum map becomes a value of the modulus of a coadjoint orbit. We give a representation theoretic description of this modulus.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology · Geometric Analysis and Curvature Flows