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Conformally covariant differential symmetry breaking operators for a vector bundle of rank 3 on $S^{3}$ $S^{3}$

Víctor Pérez-Valdés

Graduate School of Mathematical Sciences, The University of Tokyo, Tokyo, Japan

https://doi.org/10.1142/S0129167X23500726Cited by:1 (Source: Crossref)

Abstract

We construct and give a complete classification of all the differential symmetry breaking operators $𝔻_{λ, ν}^{m} : C^{\infty} (S^{3}, 𝒱_{λ}^{3}) \to C^{\infty} (S^{2}, ℒ_{m, ν})$ , between the spaces of smooth sections of a vector bundle of rank $3$ over the $3$ -sphere $𝒱_{λ}^{3} \to S^{3}$ , and a line bundle over the $2$ -sphere $ℒ_{m, ν} \to S^{2}$ . In particular, we give necessary and sufficient conditions on the tuple of parameters $(λ, ν, m)$ for which these operators exist.

Communicated by Toshiyuki Kobayashi

Keywords:

AMSC: 22E45, 58J70, 22E30, 22E46, 22E47, 34A30

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