Abstract
Casimir operators for semidirect products of some semisimple groups with Heisenberg groups are computed. The analysis is carried out using dual representations on Fock space, wherein the action of the semidirect products are related to their dual groups, namely certain unitary, orthogonal, and symplectic groups. The compact symplectic group chain is also investigated; by passing to the complexification, groups `between` the symplectic groups are constructed, which are of the form of semidirect products of symplectic groups with Heisenberg groups.
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