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Symplectic induction, prequantum induction, and prequantum multiplicities
Communications in Contemporary Mathematics ( IF 1.2 ) Pub Date : 2021-05-17 , DOI: 10.1142/s0219199721500577
Tudor S. Ratiu 1, 2 , François Ziegler 3
Affiliation  

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:

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。
更新日期:2021-05-17
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