Canonical representations of Sp(1, n) associated with representations of Sp(1)

Canonical representations of Sp (1, n) associated with finite dimensional i rreducible representations of Sp(1) are defined using vector-valued Berezin kernels. Their decomposition into irreducible representations is determine d by decomposing the corresponding reproducing distributions in terms of po sitive definite trace spherical functions on Sp(1, n), The canonical repres entatons are also identified with the restriction to Sp (1, n) of certain m aximal degenerate representations of SL(n + 1, H).