Zelevinsky segment and strongly positive representations

Let G n Gₙ upper G Subscript n denote either the group S O ( 2 n + 1 , F ) $SO(2n+1, F)$ upper S upper O left parenthesis 2 n plus 1 comma upper F right parenthesis or S p ( 2 n , F ) $Sp(2n, F)$ upper S p left parenthesis 2 n comma upper F right parenthesis over a non-Archimedean local field of characteristic zero. We determine all composition factors of a parabolically induced representation of the form ⟨ [ ν a ρ , ν b ρ ] ⟩ ⋊ σ [ ν ᵃ ρ , ν ᵇ ρ ] σ left angle bracket left bracket nu Superscript a Baseline rho comma nu Superscript b Baseline rho right bracket right angle bracket right normal factor semidirect product sigma , where ⟨ [ ν a ρ , ν b ρ ] ⟩ [ ν ᵃ ρ , ν ᵇ ρ ] left angle bracket left bracket nu Superscript a Baseline rho comma nu Superscript b Baseline rho right bracket right angle bracket denotes the Zelevinsky segment representation of the general linear group attached to the segment [ ν a ρ , ν b ρ ]