Singular conformally invariant trilinear forms and generalized Rankin Cohen operators

TL;DR

This paper computes the most singular residues of conformally invariant trilinear forms on smooth functions, expressing them through new covariant bidifferential operators called generalized Rankin Cohen operators, using Bernstein-Sato identities.

Contribution

It introduces new formulas for generalized Rankin Cohen operators and computes their residues, advancing understanding of conformally invariant forms.

Findings

Explicit formulas for the most singular residues of the forms.

New expressions for covariant bidifferential operators.

Application of Bernstein-Sato identities to conformal invariance.

Abstract

The most singular residues of the standard meromorphic family of trilinear conformally invariant forms on $\mathcal C^\infty_c(\mathbb R^d)$ are computed. Their expression involves covariant bidifferential operators (generalized Rankin Cohen operators), for which new formul\ae \ are obtained. The main tool is a Bernstein-Sato identity for the kernel of the forms.