201411.6310v1 On parabolic induction on inner forms of the general linear group over a non-archimedean local field

We give new criteria for the irreducibility of parabolic induction on the general linear group and its inner forms over a local non-archimedean field. In particular, we give a necessary and sufficient condition when the inducing data is of the form π⊗σ where π is a Speh representation and σ is an arbitrary irreducible representation. As an application we simplify the proof of the ..