Symmetry breaking operators for real reductive groups of rank one

Jan Frahm, Clemens Weiske

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For a pair of real reductive groups G ⊂G we consider the space Hom G (π| G ,τ) of intertwining operators between spherical principal series representations π of G and τ of G , also called symmetry breaking operators. Restricting to those pairs (G,G ) where dim⁡Hom G (π| G ,τ)<∞ and G and G are of real rank one, we classify all symmetry breaking operators explicitly in terms of their distribution kernels. This generalizes previous work by Kobayashi–Speh for (G,G )=(O(1,n+1),O(1,n)) to the reductive pairs (G,G )=(U(1,n+1;F),U(1,m+1;F)×F) with F=C,H,O and F<U(n−m;F). In most cases, all symmetry breaking operators can be constructed using one meromorphic family of distributions whose poles and residues we describe in detail. In addition to this family, there may occur some sporadic symmetry breaking operators which we determine explicitly.

Original languageEnglish
Article number108568
JournalJournal of Functional Analysis
Number of pages70
Publication statusPublished - 15 Sept 2020


  • math.RT
  • 22E45


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  • Symmetry Breaking in Mathematics

    Frahm, J., Weiske, C., Ditlevsen, J., Spilioti, P., Bang-Jensen, F. J. & Labriet, Q.


    Project: Research

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