Characters, dual pairs, and unipotent representations (Q1175021)

This paper uses Howe's formalism of real dual reductive pairs to obtain a number of interesting results about ``unipotent'' and ``singular low rank'' representations. For example, if \((G,G')\) is such a dual pair in the ``stable range'', then the Howe lift from \(G\) to \(G'\) provides examples of irreducible unitary unipotent and singular low rank representations attached to nilpotent coadjoint orbits in a very explicit fashion; moreover, it is often possible to calculate the wave-front set of these representations explicitly in terms of the orbit [cf. \textit{R. Howe}, Automorphic forms, representation theory and arithmetic, Bombay 1979, 117-140 (1981; Zbl 0494.22010)].