ON THE INFINITE-DIMENSIONAL HIDDEN SYMMETRIES. III. qR–CONFORMAL SYMMETRIES AT qR → ∞ AND BEREZIN-KARASEV-MASLOV ASYMPTOTIC QUANTIZATION OF C ∞ (S 1)

This short paper being the continuation of the previous parts [1] belongs to the series of articles supplemental to [2], and also lies in lines of the general ideology exposed in the review [3]. The main purpose of the activity, which has its origin and motivation presumably in the author’s researches [4] on the experimentally mathematical aspects of interactively controlled systems (i.e. the controlled systems, in which the control is coupled with unknown or uncompletely known uncontrolled feedbacks) and applications, is to explicate the essentially infinite-dimensional aspects of the hidden symmetries, which appear in the representation theory of the finite dimensional Lie algebras and related algebraic structures. The present series is organized as a sequence of topics, which illustrate this basic idea on the simple and tame examples without superfluous difficulties and details as well as in the series [2] but from a bit more geometric point of view.