Invariant star products and representations of compact semisimple Lie groups (Q1823485)

Starting from the work of \textit{F. A. Berezin} [Izv. Akad. Nauk SSSR, Ser. Mat. 39, 363-402 (1975; Zbl 0312.53050)] an earlier paper by the author [Lett. Math. Phys. 11, 361-372 (1986; Zbl 0618.53049)] defined an invariant star product on every nonexceptional Kähler symmetric space. A recursion formula is obtained to calculate the corresponding invariant Hochschild 2-cochains for spaces of types II and III. An invariant star product is defined on every integral symplectic (Kähler) homogeneous space of simply-connected compact Lie groups (on every integral orbit of the coadjoint representation). The invariant 2-cochains are obtained from the Bochner-Calabi function of the space. The leading term of the \(\ell th\)-2-cochain is determined by the \(\ell\)-power of the Laplace operator.