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Abstract
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 dimHom _{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 language  English 

Article number  108568 
Journal  Journal of Functional Analysis 
Volume  279 
Issue  5 
Number of pages  70 
ISSN  00221236 
DOIs  
Publication status  Published  15 Sept 2020 
Keywords
 math.RT
 22E45
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Symmetry Breaking in Mathematics
Frahm, J., Weiske, C., Ditlevsen, J., Spilioti, P., BangJensen, F. J. & Labriet, Q.
01/08/2019 → 31/07/2024
Project: Research