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

TL;DR

This paper explores the harmonic representation of the group SU(p,q) using complex Weyl correspondence, providing explicit formulas and extending results to related group structures.

Contribution

It introduces explicit formulas for complex Weyl symbols of harmonic representation operators of SU(p,q) and extends these results to a semi-direct product involving the Heisenberg group.

Findings

Derived explicit formulas for complex Weyl symbols of harmonic operators

Extended harmonic representation results to a semi-direct product group

Connected harmonic analysis with complex Weyl correspondence on Fock space

Abstract

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 $SU(p,q)$.