Complex Weyl symbols of metaplectic operators: an elementary approach

2023/06/22 by Benjamin Cahen, Cahen, Benjamin · 1 citation
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2306.12947

openalex publication_date 2023/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give explicit formulas for the Berezin symbols and the complex Weyl symbols of the metaplectic representation operators by using the holomorphic representations of the Jacobi group. Then we recover some known formulas for the symbols of the metaplectic operators in the classical Weyl calculus, in particular for the classical Weyl symbol of the exponential of an operator whose Weyl symbol is a quadratic form.

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