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

Abstract

Abstract We study the formal geometric quantization of

$$b^m$$

b m

-symplectic manifolds equipped with Hamiltonian actions of a torus T with nonzero leading modular weight. The resulting virtual

$$T-$$

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.