Some bounds on unitary duals of classical groups‎ - ‎non-archimeden case

We first give bounds for domains where the unitarizabile subquotients can show up in the parabolically induced representations of classical p-adic groupsý. ýRoughlyý, ýthey can show up only if theý ýcentral character of the inducing irreducible cuspidal representation is dominated by theý ýsquare root of the modular character of the minimal parabolic subgroupý. ýFor unitarizable subquotients supported by a fixed parabolic subgroupý, ýor in a specific Bernstein componentý, ýa more precise bound is givený.
ýFor the reductive groups of rank at least twoý, ýthe trivial representation is always isolated in the unitary dual (Dý. ýKazhdan)ý. ýStillý, ýwe may ask if the level of isolation is higher in the case of the automorphic dualsý, ýas it is a case in the rank oneý. ýWe show that the answer is negative to this question for symplectic p-adic groupsý.