On a remark by Alan Weinstein

Abstract

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.

16 pages, to appear in Contemporary Mathematics, Proceedings of the AMS-EMS-SMF conference, special section on Diffeology, Grenoble 2022