Symplectic induction, prequantum induction, and prequantum multiplicities

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