Polynomial quantization and overalgebra
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.
scientific article; zbMATH DE number 6952716