The complex Weyl calculus as a Stratonovich-Weyl correspondence for the real diamond group

Benjamin Cahen

doi:10.21099/tkbjm/20204401121

Abstract

We revisit the problem of constructing a Stratonovich-Weyl correspondence for each generic representation of a the real diamond group which was already considered in [B. Cahen, Riv. Mat. Univ. Parma 4 (2013), 197-213]. Here we use the complex Weyl calculus on the Fock space. This allows us, in particular, to obtain some closed formulas for the Stratonovich-Weyl symbols of the representation operators.

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Benjamin Cahen. "The complex Weyl calculus as a Stratonovich-Weyl correspondence for the real diamond group." Tsukuba J. Math. 44 (1) 121 - 137, July 2020. https://doi.org/10.21099/tkbjm/20204401121

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Published: July 2020

First available in Project Euclid: 22 December 2020

MathSciNet: MR4194195

Digital Object Identifier: 10.21099/tkbjm/20204401121

Subjects:

Primary: 22E45 , 22E70 , 81R05 , 81R30 , 81S10

Keywords: Bargmann-Fock representation , Berezin quantization , coadjoint orbit , coherent states , Complex Weyl calculus , diamond group , Fock space , Heisenberg group , ‎reproducing kernel Hilbert ‎space , Stratonovich-Weyl correspondence

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