Geodesic
Quantization commutes with reduction in the non-compact setting: the case of holomorphic discrete series
Journal of the European Mathematical Society, Tome 17 (2015) no. 4, pp. 955-990.

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In this paper we show that the multiplicities of holomorphic discrete series representations relative to reductive subgroups satisfy the credo “quantization commutes with reduction”.
DOI : 10.4171/jems/523
Classification : 58-XX, 00-XX, 19-XX, 57-XX
Keywords: Holomorphic discrete series, moment map, reduction, geometric quantization, transversally elliptic symbol 
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     author = {Paul-Emile Paradan},
     title = {Quantization commutes with reduction in the non-compact setting: the case of holomorphic discrete series},
     journal = {Journal of the European Mathematical Society},
     pages = {955--990},
     publisher = {mathdoc},
     volume = {17},
     number = {4},
     year = {2015},
     doi = {10.4171/jems/523},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/523/}
}
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Paul-Emile Paradan. Quantization commutes with reduction in the non-compact setting: the case of holomorphic discrete series. Journal of the European Mathematical Society, Tome 17 (2015) no. 4, pp. 955-990. doi : 10.4171/jems/523. http://geodesic.mathdoc.fr/articles/10.4171/jems/523/

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