In this paper we show that the multiplicities of holomorphic discrete series representations relative to reductive subgroups satisfy the credo “quantization commutes with reduction”.
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Paul-Emile Paradan, Quantization commutes with reduction in the non-compact setting: the case of holomorphic discrete series. J. Eur. Math. Soc. 17 (2015), no. 4, pp. 955–990DOI 10.4171/JEMS/523