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.
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