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Let A be a finite dimensional central division algebra over a localnon-archimedean field F. Fix any parabolic subgroup P of GL(n,A) and a Levifactor M of P. Let \pi be an irreducible unitary representation of M and \phi(not necessarily unitary) character of M. We give an explicit necessary andsufficient condition for the parabolically induced representation Ind(\phi\pi)of GL(n,A) to be irreducible.

Irreducibility criterion for representations induced by essentially unitary ones (case of non-archimedean GL(n,A)