Commentarii Mathematici Helvetici


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Volume 80, Issue 4, 2005, pp. 795–810
DOI: 10.4171/CMH/35

Invariant *-products on coadjoint orbits and the Shapovalov pairing

Anton Alekseev (1) and A. Lachowska (2)

(1) Section de Mathématiques, Université de Genève, 2-4, rue du Lièvre, C.P. 240, 1211, GENÈVE, SWITZERLAND
(2) Institut de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, SB IMB CAG, Batiment MA C2 604, Station 8, 1015, LAUSANNE, SWITZERLAND

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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