Complex Weyl correspondence and harmonic representation of $SU(p,q)$

We study the harmonic representation of $SU(p,q)$ in connection to the complex Weyl correspondence on the Fock space. In particular, we give explicit formulas for the complex Weyl symbols of the harmonic representation operators. Similar results are also obtained for the extended harmonic representation of the semi-direct product of the $(2p+2q+1)$-dimensional Heisenberg group by $SU(p,q)$.