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

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