The unitarizability of the Aubert dual of strongly positive square integrable representations

Under a natural assumption, which holds in the generic case, we prove in this paper that, for the classical p-adic groups, the Aubert dual of an irreducible, strongly positive square-integrable representation (in the sense of Mœgl., in-Tadić classification), is unitarizable. In this way, for this important class of representations, we verify the conjecture which states that the Aubert involution preserves unitarity.