Radial BPZ equations and partition functions of FK-Ising interfaces conditional on one-arm event

Abstract: Radial BPZ equations come naturally when one solves Dub\'{e}dat's commutation relation in the radial setting. We construct positive solutions to radial BPZ equations and show that partition functions of FK-Ising interfaces in a polygon conditional on a one-arm event are positive solutions to radial BPZ equations.