In this paper we prove the unitarity of duals of tempered representations supported on minimal parabolic subgroups for split classical $p$-adic groups. We also construct a family of unitary spherical representations for real and complex classical groups

MSC Classifications:

22E35, 22E50, 11F70 show english descriptions Analysis on $p$-adic Lie groups
Representations of Lie and linear algebraic groups over local fields [See also 20G05]
Representation-theoretic methods; automorphic representations over local and global fields 22E35 - Analysis on $p$-adic Lie groups
22E50 - Representations of Lie and linear algebraic groups over local fields [See also 20G05]
11F70 - Representation-theoretic methods; automorphic representations over local and global fields

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