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Frobenius reciprocity asserts that induction from a subgroup and restrictionto it are adjoint functors in categories of unitary G-modules. In the 1980s,Guillemin and Sternberg established a parallel property of HamiltonianG-spaces, which (as we show) unfortunately fails to mirror the situation wheremore than one G-module "quantizes" a given Hamiltonian G-space. This paperoffers evidence that the situation is remedied by working in the category of*prequantum* G-spaces, where this ambiguity disappears; there, we defineinduction and multiplicity spaces, and establish Frobenius reciprocity as wellas the "induction in stages" property.

Symplectic Induction, Prequantum Induction, and Prequantum Multiplicities