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A momentum map for the Heisenberg group

Richard Cushman

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.

A momentum map for the Heisenberg group

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.
Paper Structure (4 sections, 44 equations)

This paper contains 4 sections, 44 equations.

Table of Contents

  1. The affine group ${\mathbb{R} }^{2n}$
  2. Coadjoint orbits of ${\mathrm{H}}_{2n+1}$
  3. The momentum mapping of ${\mathrm{H}}_{2n+1}$
  4. Representation of $\mathfrak{h}$ corresponding to ${\mathcal{O}}_1$