Ratiu, Tudor S.Ziegler, Francois2022-05-232022-05-232022-05-232022-05-0110.1142/S0219199721500577https://infoscience.epfl.ch/handle/20.500.14299/188096WOS:000789113100009Frobenius 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.Mathematics, AppliedMathematicsMathematicssymplectic manifoldprequantum bundlelie group actionmomentum mapreductioninductionmultiplicityfrobenius reciprocitycoadjoint orbitunitary representationstext::journal::journal article::research article