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Abstract
The two-sheeted hyperboloid \(\mathcal{L}\) in ℝn can be identified with the unit sphere Ω in ℝn with the equator removed. Canonical representations of the group G = SO 0(n − 1, 1) on \(\mathcal{L}\) are defined as the restrictions to G of the representations of the overgroup \(\tilde G\) = SO 0(n, 1) associated with a cone. They act on functions and distributions on the sphere Ω. We decompose these canonical representations into irreducible constituents and decompose the Berezin form. Bibliography: 12 titles.
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