Residue formula for regular symmetry breaking operators

Abstract

We prove an explicit residue formula for a meromorphic continuation of conformally covariant integral operators between differential forms on ${\mathbf{R}}^n$ and on its hyperplane. The results provide a simple and new construction of the conformally covariant differential symmetry breaking operators between differential forms on the sphere and those on its totally geodesic hypersurface that were introduced in [Kobayashi-Kubo-Pevzner, Lect. Notes Math. (2016)]. Moreover, we determine the zeros of the matrix-valued regular symmetry breaking operators between principal series representations of $O(n+1,1)$ and $O(n,1)$.

References in corpus (1)

• Symmetry breaking for orthogonal groups and a conjecture by B. Gross and D. Prasad

Cited by in corpus (3)

• Conformal symmetry breaking on differential forms and some applications
• A short proof for Rankin--Cohen brackets and generating operators
• Recent advances in branching problems of representations