Abstract:
Canonical representations of Sp(1,n) associated with finite dimensional irreducible representations of Sp(1) are defined using vector-valued Berezin kernels. Their decomposition into irreducible representations is determined by decomposing the corresponding reproducing distributions in terms of positive definite trace spherical functions on Sp(1,n). The canonical representatons are also identified with the restriction to Sp(1,n) of certain maximal degenerate representations of SL(n+1,H).
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Received: 1 May 1998 / Accepted: 18 November 1998
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van Dijk, G., Pasquale, A. Canonical Representations of Sp(1,n) Associated with Representations of Sp(1). Comm Math Phys 202, 651–667 (1999). https://doi.org/10.1007/s002200050600
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DOI: https://doi.org/10.1007/s002200050600