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Invariant Measures on Polarized Submanifolds in Group Quantization

J. Guerrero·V. Aldaya
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Abstract

We provide an explicit construction of quasi-invariant measures on polarized coadjoint orbits of a Lie group G. The use of specific (trivial) central extensions of G by the multiplicative group ${R}^+$ allows us to restore the strict invariance of the measures and, accordingly, the unitarity of the quantization of coadjoint orbits. As an example, the representations of $SL(2,\Real)$ are recovered.

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J. Guerrero, V. Aldaya. 2000-03-22. Invariant Measures on Polarized Submanifolds in Group Quantization. https://doi.org/10.1063/1.1288497

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