Polynomial quantization and overalgebra
type: Item
instance of: scholarly article
title: Polynomial quantization and overalgebra
zbMATH Open document ID: 1400.43004
published in: Algebras and Representation Theory
publication date: 2018-10-12T00:00:00Z
review text: In the paper under review, the author uses the reproducing function approach together with a new approach based on the notion of overgroup to give a modification of the polynomial quantization of a para-Hermitian symmetric space. The advantage of the overgroup approach is that both covariant and contravariant symbols and the Berezin transform appear naturally which leads to the fact that the polynomial quantization can be understood as a representation, theoretically. Moreover, it is shown that the multiplication of symbols can be described in terms of the action of an overalgebra.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 43A85
Mathematics Subject Classification ID: 22E46
zbMATH DE Number: 6952716
zbMATH Keywords: symplectic manifolds
zbMATH Keywords: symbol calculus
zbMATH Keywords: quantization
zbMATH Keywords: Berezin transform
author: V. F. Molchanov
MaRDI profile type: Publication
full work available at URL: s10468-018-9784-6
OpenAlex ID: W2803123035
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cites work: The action of an overalgebra on the Plancherel decomposition and shift operators in the imaginary direction
DOI: 10.1007/S10468-018-9784-6
description: scientific article; zbMATH DE number 6952716