Abstract: Atiyah and Bott famously showed that Borel-Weil-Bott and the equivariant localization theorem for the flag manifold imply a proof of the Weyl-Character formula. I'll explain how generalizing this in a certain way to some infinite dimensional Kac-Moody requires that certain limits be switched for some infinite-dimensional varieties, together with an idea of Graeme Segal, and give some new sufficient conditions for when this may be done. This all sounds a bit technical, but I really won't assume very much.