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Coherent state representations. A survey

Authors
Publisher
Elsevier Ltd
Publication Date
Volume
35
Identifiers
DOI: 10.1016/0034-4877(96)89292-5
Keywords
  • Coherent State Representation
  • Highest Weight Representation
  • Metaplectic Representation
  • Momentum Mapping
  • Homogeneous Kähler Manifold
Disciplines
  • Mathematics

Abstract

Abstract The coherent state (CS) representation of a Lie group G is an irreducible unitary representation such that G has a complex orbit on the projective space corresponding to the representation space. We show how the fact that any representation of a compact Lie group is a CS representation leads to the orbit method for such groups. Next, we describe CS representations of Heisenberg groups and semisimple groups of Hermitian type. Finally, we sketch a proof of the theorem that a unimodular Lie group which admits CS representations is locally isomorphic to a semidirect product of a Heisenberg group and a group of Hermitian type.

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