Projections of measures on nilpotent orbits and asymptotic multiplicities of \(K\)-types in rings of regular functions. II (Q1915344)

This article is a continuation of [the author, Pac. J. Math. 170, 161-202 (1995; see the preceding review)]. The author continues his program of proving a conjecture of Vogan that the asymptotic behavior of \(K\)-types in the coordinate ring of a real nilpotent coadjoint orbit is determined by the (pushforward of) Liouville measure on the orbit by showing that the set of complex orbits for which the conjecture holds is closed under induction. He also shows, in both the real and complex cases, that the conjecture holds for nilpotent orbits of minimal nonzero dimension and relates it to a recent unpublished result of Schmid and Vilonen establishing a connection between the asymptotic support and characteristic variety of a Harish-Chandra module.