For every semisimple coadjoint orbit of a complex connected semisimple Lie group , we obtain a family of -invariant products on the space of holomorphic functions on . For every semisimple coadjoint orbit of a real connected semisimple Lie group , we obtain a family of -invariant products on a space of certain analytic functions on by restriction. , endowed with one of the products , is a -Fréchet algebra, and the formal expansion of the products around determines a formal deformation quantization of , which is of Wick type if is compact. Our construction relies on an explicit computation of the canonical element of the Shapovalov pairing between generalized Verma modules and complex analytic results on the extension of holomorphic functions.
Cite this article
Philipp Schmitt, Strict quantization of coadjoint orbits. J. Noncommut. Geom. 15 (2021), no. 4, pp. 1181–1249DOI 10.4171/JNCG/429