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

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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.
minor comments are inserted into the revised version; Part I:funct-an/9612004, II:funct-an/9701009

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