T. Kobayashi and B. Speh. Symmetry breaking for orthogonal groups and a conjecture by B. Gross and D. Prasad. In W. Müller, S. Shin, and N. Templier, editors, SSTF 2016: Geometric Aspects of the Trace Formula, Simons Symposium on the Trace Formula, pages 245-266. Springer, Cham, 2018. Published online: 12 October 2018. Print ISBN: 978-3-319-94832-4. Online ISBN: 978-3-319-94833-1. arXiv: 1702.00263. DOI: 10.1007/978-3-319-94833-1_8..

We consider irreducible unitary representations Ai of G=SO(n+1,1) with the same infinitesimal character as the trivial representation and representations Bj of H=SO(n,1) with the same properties and discuss H-equivariant homomorphisms HomH(Ai,Bj). For tempered representations our results confirm the predictions of conjectures by B. Gross and D. Prasad.

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