  Geometric Quantization links holomorphic geometry with real geometry, a
relation that is a prototype for the modern development of mirror symmetry. We
show how to use this treatment to construct a special basis in every space of
conformal blocks. This is a direct generalization of the basis of theta
functions with characteristics in every complete linear system on an Abelian
variety (see Mumford's "Tata lectures on theta" cite(Mumford)). The same
construction generalizes the classical theory of theta functions to vector
bundles of higher rank on Abelian varieties and K3 surfaces. We also discuss
the geometry behind these constructions.
