A generating operator for Rankin-Cohen brackets
Complex Variables
2025-06-16 v2 Representation Theory
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.
Cite
@article{arxiv.2306.16800,
title = {A generating operator for Rankin-Cohen brackets},
author = {Toshiyuki Kobayashi and Michael Pevzner},
journal= {arXiv preprint arXiv:2306.16800},
year = {2025}
}