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28 March 2024
 
  » arxiv » math.DG/0411334

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On the BKS pairing for Kahler quantizations of the cotangent bundle of a Lie group
Carlos Florentino ; Pedro Matias ; Jose Mourao ; Joao P. Nunes ;
Date 15 Nov 2004
Subject Differential Geometry; Symplectic Geometry MSC-class: 81S10; 53D50; 22E30 | math.DG math.SG
AbstractA natural one-parameter family of Kahler quantizations of the cotangent bundle $T^*K$ of a compact Lie group $K$, taking into account the half-form correction, was studied in cite{FMMN}. In the present paper, it is shown that the associated Blattner-Kostant-Sternberg (BKS) pairing map is unitary and coincides with the parallel transport of the quantum connection introduced in our previous work, from the point of view of cite{AdPW}. The BKS pairing map is a composition of (unitary) coherent state transforms of $K$, introduced in cite{Ha1}. In the limit when one of the Kähler polarizations degenerates to the vertical real polarization, our results reproduce the unitarity up to scaling of the appropriate BKS pairing map, established by Hall.
Source arXiv, math.DG/0411334
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