For any special nilpotent orbit, let $\frac{ 1}{ 2}h^{ \vee}$ be one half of the semisimple element of a Jacobson-Morozov triple associated to the orbit. In 1985, Barbasch and Vogan defined the notion of special unipotent representations with infinitesimal character $(\frac{ 1}{ 2}h^{ \vee},\frac{ 1}{ 2}h^{ \vee})$. Some properties of such representations were discovered when $\frac{ 1}{ 2}h^{ \vee}$ is integral. In this manuscript, we give a complete proof of these properties when $\frac{ 1}{ 2}h^{ \vee}$ is not integral.
Categories: math.RT