Symplectic model for Zelevinsky modules of GL(n,D)

Abstract: Let D be a quaternion division algebra over a non-archimedean local field F of characteristic zero. This article demonstrates the existence and uniqueness of the symplectic model for a family of Zelevinsky modules of GL(n, D) to a family of irreducible representations of GL(n, D). For this family of irreducible representations, we identify a necessary condition under which a symplectic model can exist. This work extends a result of Offen and Sayag beyond the case D = F.