Harmonic Analysis · Symplectic Geometry · Geometric Quantization · K-Theory and Homology · Index Theory · Representation Theory · Equivariant Topology

## General Idea

Also called ‘*quantization commutes with reduction*’. There are many different formulations of the conjecture and versions of the theorem. Maybe better called a *principle*.

## References

For singular symplectic quotients, and on the arithmetic genus of a Hamiltonian $G$-manifold

- Eckhard Meinrenken, Reyer Sjamaar.
*Singular Reduction and Quantization*https://arxiv.org/abs/dg-ga/9707023

For noncompact groups and spaces, without using $S\text{pin}^c$ Dirac operator but using equivariant $K$-homology, so related to Baum-Connes

- P. Hochs, N.P. Landsman.
*The Guillemin-Sternberg conjecture for noncompact groups and spaces*https://arxiv.org/abs/math-ph/0512022

Related to the orbit method and Harish-Chandra theorem, hence with geometric representation theory

- Michel Duflo, Michèle Vergne.
*Kirillov’s formula and Guillemin-Sternberg conjecture*https://arxiv.org/abs/1110.0987

In the setting of shifted symplectic structures, a derived analog of the principle.

- Pavel Safronov.
*Shifted geometric quantization*https://arxiv.org/abs/2011.05730