On $A$-parameters containing unitary lowest weight representations of $\mathrm{U}(p,q)$

In this paper, we determine all the Arthur packets containing an irreducible unitary lowest weight representation $\pi$ of real unitary group $G=\mathrm{U}(p,q)$, including non-scalar cases. Our methods are the Barbasch-Vogan parametrization of representations of $G$ and Trapa’s algorithm to calculate the cohomologically induced representations. In particular, we show that an Arthur packet has at most one irreducible unitary lowest weight representation of $G$. As a consequence, if an irreducible unitary lowest weight representation $\pi$ exists in the Arthur packet of $\psi$, we give an explicit formula of the lowest $K$-type of $\pi$.