On representations ofp-adicGL2(D)

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This paper is in two parts. In the first we work out the asymptotics of functions in the Kirillov model of an irreducible admissible representation of GL 2 (D) for a p-adic division algbera D. In the second part we prove a theorem, for GL m (H) for a quaternionic p-adic division algebra H, of explicitly realizing the contragredient representation and then derive a consequence of this for distinguished representations for GL 2 (H]).