  In an earlier paper we propose an approach to the unitarizability problem in
the case of classical groups over a p-adic field of characteristic zero based
on cuspidal reducibility points. We have reduced earlier the unitarizability
for these groups to the case of so called weakly real representations.
Following C. Jantzen, to an irreducible weakly real representation $\pi$ of a
classical group one can attach a sequence ($\pi_1,\dots,\pi_k)$ of irreducible
representations of classical groups, each of them supported by a line of
cuspidal representations $X_\rho$ of general linear groups containing a
selfcontragredient representation $\rho$, and an irreducible cuspidal
representation $\sigma$ of a classical group. The first question is if $\pi$ is
unitarizable if and only if all $\pi_i$ are unitarizable.
  Further, the pair $\rho,\sigma$ determines the non-negative reducibility
exponent $\alpha_{\rho,\sigma}\in\frac12\mathbb Z$ among $\rho$ and $\sigma$.
The question is if the unitarizability of irreducible representations supported
by $X_\rho\cup \sigma$ depends only on $\alpha_{\rho,\sigma}$.
  Following the above proposed strategy, in this paper we solve the
unitarizability problem for irreducible subquotients of representations
Ind$_P^G(\tau)$, where G is a classical group over a p-adic field of
characteristic zero, P is a parabolic subgroup of G of the generalized rank (at
most) 3 and $\tau$ is an irreducible cuspidal representation of a Levi factor M
of P. As a consequence, this gives also a solution of the unitarizability
problem for classical p-adic groups of the split rank (at most) three. This
paper also provides some very limited support for the possibility of the above
approach to the unitarizability could work in general.

Representation Theory