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arXiv · 2007.09434

Symplectic Induction, Prequantum Induction, and Prequantum Multiplicities

Tudor S. Ratiu·Francois Ziegler
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Abstract

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.

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Tudor S. Ratiu, Francois Ziegler. 2020-07-18. Symplectic Induction, Prequantum Induction, and Prequantum Multiplicities. https://doi.org/10.1142/s0219199721500577

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