  In the monograph arXiv:2108.03453, we define the notion of a unipotent
representation of a complex reductive group. The representations we define
include, as a proper subset, all special unipotent representations in the sense
of Barbasch-Vogan and form the (conjectural) building blocks of the unitary
dual. In arXiv:2108.03453 we provide combinatorial formulas for the
infinitesimal characters of all unipotent representations of linear classical
groups. In this paper, we establish analogous formulas for spin and exceptional
groups, thus completing the determination of the infinitesimal characters of
all unipotent ideals. Using these formulas, we prove an old conjecture of
Vogan: all unipotent ideals are maximal. For $G$ a real reductive Lie group
(not necessarily complex), we introduce the notion of a unipotent
representation attached to a rigid nilpotent orbit (in the complexified Lie
algebra of $G$). Like their complex group counterparts, these representations
form the (conjectural) building blocks of the unitary dual. Using the atlas
software (and the work of Adams-Miller-van Leeuwen-Vogan) we show that if $G$
is a real form of a simple group of exceptional type, all such representations
are unitary.
