Rankin-Cohen brackets on tube-type domains
arXiv:2003.06133 · doi:10.2140/tunis.2021.3.551
Abstract
A new formula is obtained for the holomorphic bi-differential operators on tube-type domains which are associated to the decomposition of the tensor product of two scalar holomorphic representations, thus generalizing the classical Rankin-Cohen brackets. The formula involves a family of polynomials of several variables which may be considered as a (weak) generalization of the classical Jacobi polynomials.
arXiv commentIn this new version, the proof of the main theorem has been changed. The new proof makes the paper more self-contained