ABSTRACT
This chapter shows that it is possible to construct harmonic forms at the expense of modifying the representation. In order to construct harmonic forms, a limiting process is required and in the limit the isomorphism class of the locally constant Hilbert bundle may no longer be preserved. The chapter presents the case of infinite-dimensional separable Hilbert spaces. Except for minor modifications, the proof is the same as in the case of finite-dimensional unitary representations. The same notation applies to differential forms taking values in a Hilbert space. The chapter explains methods of fibering compact Kahler manifolds over projective varieties of the general type, including the method of using equivariant holomorphic 1-forms.
