Proceedings of the Japan Academy, Series A, Mathematical Sciences
- Proc. Japan Acad. Ser. A Math. Sci.
- Volume 93, Number 8 (2017), 86-91.
Symmetry breaking operators for the restriction of representations of indefinite orthogonal groups $O(p,q)$
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].
Proc. Japan Acad. Ser. A Math. Sci. Volume 93, Number 8 (2017), 86-91.
First available in Project Euclid: 3 October 2017
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Digital Object Identifier
Primary: 22E46: Semisimple Lie groups and their representations
Secondary: 33C45: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) [See also 42C05 for general orthogonal polynomials and functions] 53C35: Symmetric spaces [See also 32M15, 57T15]
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