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 GL2(𝒟) for a p-adic division algbera 𝒟. In
the second part we prove a theorem, for GLn(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
GL2(ℋ).