In mathematics, more specifically in the context of
geometric quantization, quantization commutes with reduction states that the space of global sections of a line bundle L satisfying the quantization condition[1] on the
symplectic quotient of a compact
symplectic manifold is the space of invariant
sections[vague] of L.
This was conjectured in 1980s by Guillemin and Sternberg and was proven in 1990s by Meinrenken[2][3] (the second paper used
symplectic cut) as well as Tian and Zhang.[4] For the formulation due to Teleman, see C. Woodward's notes.
Meinrenken, Eckhard (1996), "On Riemann-Roch formulas for multiplicities", Journal of the American Mathematical Society, 9 (2): 373–389,
doi:10.1090/S0894-0347-96-00197-X,
MR1325798.