Polynomial Quantization on Rank One Para-Hermitian Symmetric Spaces |
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Authors: | V F Molchanov N B Volotova |
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Institution: | (1) Tambov State University, Internatsionalnaya 33, 392622 Tambov, Russia |
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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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Keywords: | Lie groups Lie algebras representations semi-simple symmetric spaces tensor products quantization symbol calculus Berezin transform |
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