Alan Weinstein remarked that, working in the framework of diffeology, a construction from Noncommutative Differential Geometry might provide the non-trivial representations required for the geometric quantisation of a symplectic structure which is not integral. In this note we show that the construction we gave with P. Antonini does indeed provide non-trivial representations.
National and Kapodistrian University of Athens, Department of Mathematics (+30) 210-7276423 Panepistimiopolis Zografou Athens, ZipCode 157-84 iandroul@math.uoa.gr
