Abstract
We construct the polynomial quantization on the space G/H where G=SL(n,R),H=GL(n−1,R). It is a variant of quantization in the spirit of Berezin. In our case covariant and contravariant symbols are polynomials on G/H. We introduce a multiplication of covariant symbols, establish the correspondence principle, study transformations of symbols (the Berezin transform) and of operators. We write a full asymptotic decomposition of the Berezin transform.
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