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Let  F  be a non-Archimedean local field of characteristic 0, and let  D  be a finite-dimensional central division algebra over  F . We prove that any unitary irreducible smooth representation of a Levi subgroup of GL  m  ( D ), with  m  ≧ 1, induces irreducibly to GL  m  ( D ). This ends the classification of the unitary dual of GL  m  ( D ) initiated by Tadić.

Proof of the Tadić conjecture (U0) on the unitary dual of GL m ( D )