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.
"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