Proc. Japan Acad. Ser. A Math. Sci. 93 (8), 86-91, (October 2017) DOI: 10.3792/pjaa.93.86
Toshiyuki Kobayashi, Alex Leontiev
KEYWORDS: representation theory, Reductive group, branching law, broken symmetry, conformal geometry, symmetry breaking operator, 22E46, 33C45, 53C35
For the pair $(G, G') =(O(p+1, q+1), O(p,q+1))$, we construct and give a complete classification of intertwining operators (symmetry breaking operators) between most degenerate spherical principal series representations of $G$ and those of the subgroup $G'$, extending the work initiated by Kobayashi and Speh [Mem. Amer. Math. Soc. 2015] in the real rank one case where $q=0$. Functional identities and residue formulæ of the regular symmetry breaking operators are also provided explicitly. The results contribute to Program C of branching problems suggested by the first author [Progr. Math. 2015].