Scattered representations of $SL(n, \mathbb{C})$

Abstract

Let $G$ be $SL(n, \mathbb{C})$. This paper aims to describe the Zhelobenko parameters and the spin-lowest $K$-types of the scattered representations of $G$, which lie at the heart of $\hat{G}^d$ - the set of all the equivalence classes of irreducible unitary representations of $G$ with non-vanishing Dirac cohomology. As a consequence, we will verify a couple of conjectures of the first-named author for $G$.