Analysis on the minimal representation of O(p,q) -- II. Branching laws

Details Analysis on the minimal representation of O(p,q) -- II. Branching laws Analysis on the minimal representation of O(p,q) -- II. Branching laws

2001-11-07

arxiv.org/abs/math/0111085v1

Adv. Math., 180 (2003), 513-550

Mathematics

Representation Theory

27 pages

Scientific paper

10.1016/S0001-8708(03)00013-6

This is a second paper in a series devoted to the minimal unitary representation of O(p,q). By explicit methods from conformal geometry of pseudo-Riemannian manifolds, we find the branching law corresponding to restricting the minimal unitary representation to natural symmetric subgroups. In the case of purely discrete spectrum we obtain the full spectrum and give an explicit Parseval-Plancherel formula, and in the general case we construct an infinite discrete spectrum.

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