Generating operators of symmetry breaking -- from discrete to continuous
arXiv:2307.16587 · doi:10.1016/j.indag.2024.03.007
Abstract
Based on the "generating operator" of the Rankin--Cohen brackets introduced in Kobayashi-Pevzner [arXiv:2306.16800], we present a method to construct various fundamental operators with continuous parameters such as invariant trilinear forms on infinite-dimensional representations, the Fourier and the Poisson transforms on the anti-de Sitter space, and integral symmetry breaking operators for the fusion rules, among others, out of a countable set of differential symmetry breaking operators.
To appear in Indagationes Mathematicae