On the infinite-dimensional hidden symmetries. III. $q_R$-conformal symmetries at $q_R\to\infty$ and Berezin-Karasev-Maslov asymptotic quantization of $C^\infty(S^1)$

TL;DR

This paper explores the connections between infinite-dimensional $q_R$-conformal symmetries at the limit $q_R oty$, Berezin quantization of the Lobachevskii plane, and Karasev-Maslov asymptotic quantization, highlighting aspects of approximate representation theory.

Contribution

It elucidates the relations between $q_R$-conformal symmetries, Berezin quantization, and asymptotic quantization, advancing understanding of their interplay in infinite-dimensional geometry.

Findings

Established links between $q_R$-conformal symmetries and Berezin quantization.

Analyzed the role of asymptotic quantization in infinite-dimensional settings.

Discussed aspects of approximate representation theory in this context.

Abstract

The relations between the infinite dimensional geometry of $q_R$-conformal symmetries at $q_R\to\infty$, Berezin quantization of the Lobachevskii plane and Karasev-Maslov asymptotic quantization are explicated. Some aspects of the ``approximate'' representation theory are discussed.