A generating operator for Rankin-Cohen brackets

Abstract

Motivated by the classical ideas of generating functions for orthogonal polynomials, we initiate a new line of investigation on "generating operators" for a family of differential operators between two manifolds. We prove a novel formula of the generating operators for the Rankin-Cohen brackets by using higher-dimensional residue calculus. Various results on the generating operators are also explored from the perspective of infinite-dimensional representation theory.