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• W2902249700 abstract "We consider the meromorphic continuation of an integral transform that gives rise to a conformally covariant, symmetry breaking operator ({mathbb {A}}_{lambda , nu }) between the natural family of representations (I(lambda )) and (J(nu )) of the indefinite orthogonal group (G=O(p+1,q+1)) and its subgroup (G'=O(p,q+1)), respectively, realized in function spaces on the conformal compactifications of flat pseudo-Riemannian manifolds ({mathbb {R}}^{p,q} supset {mathbb {R}}^{p-1,q}). In this article, we determine explicitly the image of the renormalized operator ({mathbb {A}}_{lambda , nu }) for all ((lambda , nu ) in {mathbb {C}}^2). In particular, the complex parameters ((lambda , nu )) for which the image of ({mathbb {A}}_{lambda , nu }) coincides with ({0}), ({mathbb {C}}), finite-dimensional representations, the minimal representation, or discrete series representations for pseudo-Riemannian space forms are explicitly classified. A graphic description of the K-types of the image is also provided. Our results extend a part of the prior results of Kobayashi and Speh [Memoirs of Amer. Math. Soc. 2015] in the Riemannian case where (q=0)." @default.
• W2902249700 created "2018-12-11" @default.
• W2902249700 creator A5022448902 @default.
• W2902249700 creator A5041756388 @default.
• W2902249700 date "2018-01-01" @default.
• W2902249700 modified "2023-09-30" @default.
• W2902249700 title "Image of Conformally Covariant, Symmetry Breaking Operators for $${mathbb {R}}^{p,q}$$" @default.
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• W2902249700 doi "https://doi.org/10.1007/978-981-13-2715-5_1" @default.
• W2902249700 hasPublicationYear "2018" @default.
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