Arthur–Barbasch–Vogan unitarity conjecture for special unipotent representations

Let $G_{d53f}$ be the real points of a connected reductive complex algebraic group, and let $X$ be an irreducible $(\mathfrak{g},K)$-module. If $X$ is special unipotent, meaning that its annihilator is the maximal primitive ideal $I(\mathcal{O}^\vee)$ associated with a nilpotent adjoint orbit $\mathcal{O}^\vee$ in the Lie algebra $\mathfrak{g}^\vee$ of the Langlands dual group, then

Arthur–Barbasch–Vogan conjecture. $X$ is unitarizable.

Special unipotent representations are small representations with infinitesimal character determined by one-half of the semisimple element in an $\mathfrak{sl}_2$-triple for $\mathcal{O}^\vee$. The conjecture asserts their unitarity in general; no resolution is supplied in the given text.