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Notes on the structure of quantized Hermitian symmetric spaces. (English) Zbl 0830.46068

Summary: We give a self-contained presentation of quantization theory for non- compact hermitian symmetric spaces within a non-perturbative scheme, reviewing previously established facts as needed. A number of new results are proven, with emphasis on the algebraic and structural aspects of the theory. In addition, we formulate a number of conjectures concerning the structure of the \(\mathbb{C}^*\)-algebras of quantized functions.

MSC:

46N50 Applications of functional analysis in quantum physics
46L60 Applications of selfadjoint operator algebras to physics
81S05 Commutation relations and statistics as related to quantum mechanics (general)
47N50 Applications of operator theory in the physical sciences
47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
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