  A new, configuration-space picture of a formalism of group quantization, the
GAQ formalism, is presented in the context of a previous, algebraic
generalization. This presentation serves to make a comprehensive discussion in
which other extensions of the formalism, particularly to incorporate gauge
symmetries, are developed as well. Both images are combined in order to
analyse, in a systematic manner and with complete generality, the case of
linear fields (abelian current groups). To ilustrate these developments we
particularize them for several fields and, in particular, we carry out the
quantization of the abelian Chern-Simons models over an arbitrary closed
surface in detail.
