Quantization commutes with reduction in the non-compact setting: the case of holomorphic discrete series

Paul-Emile Paradan (1)

1 IMAG - Institut Montpelliérain Alexander Grothendieck

In this paper we show that the multiplicities of holomorphic discrete series representations relatively to reductive subgroups satisfy the credo ''Quantization commutes with reduction''.

Mots clés: holomorphic discrete series; moment map; reduction; geometric quantization; transversally elliptic symbol

Domaines: Géométrie symplectique [math.SG]; Théorie des représentations [math.RT]

Paul-Emile Paradan. Quantization commutes with reduction in the non-compact setting: the case of holomorphic discrete series. Journal of the European Mathematical Society, 2015, 17 (4), pp.955-990. ⟨10.4171/JEMS/523⟩. ⟨hal-00663048⟩