We give an explicit formula for invariant -products on a wide class of coadjoint orbits. The answer is expressed in terms of the Shapovalov pairing for generalized Verma modules.
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Anton Alekseev, A. Lachowska, Invariant *-products on coadjoint orbits and the Shapovalov pairing. Comment. Math. Helv. 80 (2005), no. 4, pp. 795–810DOI 10.4171/CMH/35