  I present several applications of the Dirac inequality to the determination
of isolated unitary representations and associated "spectral gaps" in the case
of unramified principal series. The method works particularly well in order to
attach irreducible unitary representations to the large nilpotent orbits (e.g.,
regular, subregular) in the Langlands dual complex Lie algebra. The results
could be viewed as a $p$-adic analogue of Salamanca-Riba's classification of
irreducible unitary $(\mathfrak g,K)$-modules with strongly regular
infinitesimal character.
