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