On geometric quantization of $$b^m$$-symplectic manifolds

Abstract

We study the formal geometric quantization of \(b^m\)-symplectic manifolds equipped with Hamiltonian actions of a torus T with nonzero leading modular weight. The resulting virtual \(T-\)modules are finite dimensional when m is odd, as in [4]; when m is even, these virtual modules are not finite dimensional, and we compute the asymptotics of the representations for large weight.