Equivariant asymptotics for Bohr-Sommerfeld Lagrangian submanifolds

Suppose given a complex projective manifold $M$ with a fixed Hodge form $\mathrm{\Omega }$. The Bohr-Sommerfeld Lagrangian submanifolds of $(M,\mathrm{\Omega })$ are the geometric counterpart to semi-classical physical states, and their geometric quantization has been extensively studied. Here we revisit this theory in the equivariant context, in the presence of a compatible (Hamiltonian) action of a connected compact Lie group.