Moment Polyptychs and the Equivariant Quantisation of Hypertoric Varieties

We develop a method to investigate the geometric quantisation of a hypertoric variety from an equivariant viewpoint, in analogy with the equivariant Verlinde for Higgs bundles. We do this by first using the residual circle action on a hypertoric variety to construct its symplectic cut, resulting in a compact cut space which is needed for localisation. We introduce the notion of a moment polyptych associated to a hypertoric variety and prove that the necessary isotropy data can be read off from it. Finally, the equivariant Hirzebruch-Riemann-Roch formula is applied to the cut spaces and expresses the dimension of the equivariant quantisation space as a finite sum over the fixed-points. This is joint work with Johan Martens.