The purpose of this paper is to show that the multiplicities of a discrete series representation relatively to a compact subgroup can be "computed" geometrically, in the way predicted by the "qantization commutes with reduction" principle of Guillemin-Sternberg.
Transfer of characters for discrete series representations of the unitary groups in the equal rank case via the Cauchy-Harish-Chandra integral
Local periods for discrete series representations
Towards multiplicities for categories O of cyclotomic rational Cherednik algebras
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