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.

中文翻译：

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辛感应、前量子感应和前量子多重性

Frobenius 互易性断言从一个子群的归纳和对它的限制是酉类的伴随函子G-模块。在 1980 年代，Guillemin 和 Sternberg 建立了哈密顿量的平行性质G-spaces，不幸的是（正如我们所展示的）不能反映一个以上的情况G-module“量化”给定的哈密顿量G-空间。本文提供的证据表明，通过在以下类别中工作可以纠正这种情况前量子 G- 空间，这种歧义消失了；在那里，我们定义了归纳和多重空间，并建立了 Frobenius 互易性以及“阶段归纳”属性。