{Equivariant quantization of coadjoint orbits and the Shapovalov form}

In our joint paper with A. Alekseev we give an explicit formula for an equivariant star product on a wide class
of coadjoint orbits, including the orbits of semisimple elements in semisimple Lie algebras, as well as some infinite dimensional examples. The answer is given in terms of
the Shapovalov form on a generalized Verma module. I will describe the construction and discuss possible applications in representation theory.