QUATERNIONIC DISCRETE SERIES FOR Sp(1,1)

Journal article, 2009

In this paper we study the analytic realization 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) x Sp(1)). We use the Szego map to give expressions for the restrictions of the K-types occurring in the representation spaces to the submanifold AK/K.