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Where can I find details about the irreducible unitary representations of SO(1,4) and SO(2,3)?
There is Volume 2, Chapter 9 of the monumental (4-volume!) work of N. Ya. Vilenkin and A. U. Klimyk, Representations of Lie Groups and Special Functions (Kluwer, 1993).
The unitary dual of SO(1,4) was computed by Dixmier (1961); that of SO(2,3), or the locally isomorphic Sp(2,R), by Angelopoulos (1981) and Nzoukoudi (1983).
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