It has been argued that the Ashtekar-Lewandowski representation of the Ashtekar-Isham holonomy algebra is fundamental, in the sense that any other representation can be obtained by a suitable limit procedure. We propose to clarify that statement, providing, in particular, a canonical way of mapping GNS states to a family of vectors of the Ashtekar-Lewandowski Hilbert space. The so-called family of shadow states thus obtained converges, as states of the algebra, to the original GNS state.