The point of this paper is to
give a method for constructing bundle valued harmonic forms on the indefinite
Kähler symmetric space U(p + 1,q)∕U(p,q) ×U(1). Such a space of harmonic forms
has been studied by Rawnsley, Schmid and Wolf in order to unitarize certain
representations acting on Dolbeault cohomology spaces. They primiarily study a
space of “special” harmonic (0,s)-forms representing Dolbeault cohomology, and s is
the dimension of a maximal compact subvariety. Here, harmonic forms are
constructed in arbitrary degree (0,s). We construct harmonic forms corresponding to
“lowest K-types” and we determine the other possible K-types in the representation
spanned by these. We also determine when these are L2 (in an appropriate
sense).
