  In this paper we study the analytic realisation of the discrete series
representations for the group $G=Sp(1,1)$ as a subspace of the space of square
integrable sections in a homogeneous vector bundle over the symmetric space
$G/K:=Sp(1,1) /(Sp(1) \times Sp(1))$. We use the Szeg\"o map to give
expressions for the restrictions of the $K$-types occurring in the
representation spaces to the submanifold $AK/K$.
