Narrow Results

Frobenius reciprocity asserts that induction from a subgroup and restriction to it are adjoint functors in categories of unitary $G$-modules. In the 1980s, Guillemin and Sternberg established a parallel property of Hamiltonian $G$-spaces, which (as we show) unfortunately fails to mirror the situation where more than one $G$-module “quantizes” a given Hamiltonian $G$-space. This paper offers evidence that the situation is remedied by working in the category of prequantum$G$-spaces, where this ambiguity disappears; there, we define induction and multiplicity spaces and establish Frobenius reciprocity as well as the “induction in stages” property.