Guillemin-Sternberg Conjecture

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.


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

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

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

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