  Vafa-Witten theory is a twisted N=4 supersymmetric gauge theory whose
partition functions are the generating functions of the Euler number of
instanton moduli spaces. In this paper, we recall quantum gauge theory with
discrete electric and magnetic fluxes and review the main results of
Vafa-Witten theory when the gauge group is simply laced. Based on the
transformations of theta functions and their appearance in the blow-up
formulae, we propose explicit transformations of the partition functions under
the Hecke group when the gauge group is non-simply laced. We provide various
evidences and consistency checks.
