Counting irreducible representations of general linear groups and unitary groups

Let $G$ be a general linear group over $\mathbb{R}$, $\mathbb{C}$, or $\mathbb{H}$, or a real unitary group. In this paper, we precisely describe the number of isomorphism classes of irreducible Casselman-Wallach representations of $G$ with a given infinitesimal character and a given associated vari