## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### Symmetry breaking operators for the restriction of representations of indefinite orthogonal groups $O(p,q)$

#### Abstract

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].

#### Article information

Source
Proc. Japan Acad. Ser. A Math. Sci. Volume 93, Number 8 (2017), 86-91.

Dates
First available in Project Euclid: 3 October 2017

https://projecteuclid.org/euclid.pja/1506996023

Digital Object Identifier
doi:10.3792/pjaa.93.86

#### Citation

Kobayashi, Toshiyuki; Leontiev, Alex. Symmetry breaking operators for the restriction of representations of indefinite orthogonal groups $O(p,q)$. Proc. Japan Acad. Ser. A Math. Sci. 93 (2017), no. 8, 86--91. doi:10.3792/pjaa.93.86. https://projecteuclid.org/euclid.pja/1506996023

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